Coverage for local/lib/python2.7/site-packages/sage/modular/modform/periods.py : 100%

""" 

Periods of modular forms. 

""" 

# The following idea just occurred to me. 

# We could use that $\langle T_n(g), x\rangle = \langle g, T_n(x)\rangle$ 

# for any Hecke operator $T_n$, so that we only need to compute 

# the period integrals $\langle g, x_i\rangle$. Then we obtain all pairings 

# $\langle T_n(g), x_i \rangle = \langle g , T_n(x_i) \rangle$. 

# Since the $T_n(g)$ span the simple $\T$-module $S_k(\Gamma;\Q)[I]$, 

# this must give all pairings. However, it requires computing 

# only $2d$ pairings instead of $2d^2$ pairings, which is potentially 

# a huge savings when $d$ is large.