Eta Products and Models for Modular Curves
Eta Products and Models for Modular Curves
Eta Products and Models for Modular Curves
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Corollary 3.1: The leading term of the q-expansion of any<br />
delta product (associated to a fixed family) is given by<br />
∏<br />
l|N<br />
(<br />
ζ bNg/d q lg2 /d ) r l ( g<br />
d<br />
) 12rl<br />
.<br />
In particular, the ord at the corresponding cusp of the<br />
corresponding eta product is<br />
∑<br />
1<br />
l·r l<br />
24 gcd(d,N/d) d (gcd(d, N/l))2 .<br />
l|N