Space of modular forms of level 804, weight 2, and Character 804.c

• Label: 804.2.c
• Level: $804$
• Weight: $2$
• Character orbit: 804.c
• Rep. character: $\chi_{804}(671,\cdot)$
• Character field: $\Q$
• Dimension: $132$
• Newform subspaces: $2$
• Sturm bound: $272$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(272\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

	Total	New	Old
Modular forms	140	132	8
Cusp forms	132	132	0
Eisenstein series	8	0	8

Trace form

\( 132 q - 4 q^{4} - 6 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
804.2.c.a	$804$	$2$	804.c	12.b	$2$	$4$	$4$	$6.420$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-2q^{4}-\zeta_{8}^{2}q^{5}+\cdots\)
804.2.c.b	$804$	$2$	804.c	12.b	$2$	$128$	$128$	$6.420$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$