### 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.
Home