LMFDB - Space of modular forms of level 720, weight 6, and Character 720.o

Defining parameters

The following table gives the dimensions of various subspaces of $M_{6}(720, [\chi])$.

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
720.6.o.a	$720$	$6$	720.o	60.h	$2$	$4$	$4$	$115.476$	$\Q(\zeta_{8})$	$\Q(\sqrt{-1}) $		$8$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(39\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+398\zeta_{8}q^{13}+\cdots$
720.6.o.b	$720$	$6$	720.o	60.h	$2$	$8$	$8$	$115.476$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(35\beta _{2}-5\beta _{3})q^{5}-\beta _{5}q^{7}+\beta _{6}q^{11}+\cdots$
720.6.o.c	$720$	$6$	720.o	60.h	$2$	$8$	$8$	$115.476$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(5\beta _{1}-5\beta _{4})q^{5}-\beta _{2}q^{7}-7\beta _{3}q^{11}+\cdots$
720.6.o.d	$720$	$6$	720.o	60.h	$2$	$40$	$40$	$115.476$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

$ S_{6}^{\mathrm{old}}(720, [\chi]) \cong $ $S_{6}^{\mathrm{new}}(60, [\chi])$$^{\oplus 6}$$\oplus$$S_{6}^{\mathrm{new}}(120, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(240, [\chi])$$^{\oplus 2}$

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