### Known errata for "Modular Forms: A Classical and Computational
Introduction"

- p. 11: There is some weird Sage interference in the middle of a
paragraph.
- p. 19: ``We will investigate some of the arithmetic properties of the
Bernoulli numbers in''
**Section 6.1.1** (text added).
- p. 23, l.1 of proof of Porp 2.12: change "quotient group
Gamma_0(N)/SL_2(Z)" to "coset space Gamma_0(N)\backslash SL_2(Z)".
- p. 24: the enumeration of P^1(Z/8Z) is wrong, since (1:2)=(5:2) and
(3:2)=(7:2). The missing ones are (1:4) and (1:0). The coset reps
need changing accordingly.
- p. 27, first para. Once you get to (a_j g a_i^{-1})y_1=y_2 the proof
should finish thus instead of the part from "there can be no" to the
end:
Hence y_1=y_2 and a_j g = a_i; since the a's are coset reps this
implies that g=1 (and i=j) so z_1=z_2.
- p. 31, definition of *-operator: should map g to a^{-1}*g*a and not
the
other way round. Then the formula for g^* will be right. Now Gamma^*(N)
needs its definition changing too, and then the displayed calculation
becomes correct.
- p. 35 and p. 36, in the second paragraph of the proof of Theorem 2.26,
theta(g) and E_2 \cdot g should be theta(f) and E_2 \cdot f, and similarly
in the last paragraph of the proof.
- p. 47, part (1) of the proof should say that this is because an
entire function which is analytic on all of the upper half plane and
has no zeroes is constant. In part (4) of the proof: "If k < 10" should be
"if k < 12".
- p. 117, Figure 5.1: The point in lower left should be labelled ``P'', the point in the middle should be labelled ``Q'', and the point in lower right should be labelled ``P+Q''.

I would like to thank John Cremona, Pete Klimek and Ashvin Rajan for
pointing these mistakes out.

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