Space of modular forms of level 476, weight 2, and Character 476.e

• Label: 476.2.e
• Level: $476$
• Weight: $2$
• Character orbit: 476.e
• Rep. character: $\chi_{476}(475,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 476 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(476, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

\( 68 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 68 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(476, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
476.2.e.a	$476$	$2$	476.e	476.e	$2$	$8$	$8$	$3.801$	8.0.\(\cdots\).12	\(\Q(\sqrt{-17}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+2q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots\)
476.2.e.b	$476$	$2$	476.e	476.e	$2$	$20$	$20$	$3.801$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	\(\Q(\sqrt{-119}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{2}+\beta _{12}q^{3}+\beta _{8}q^{4}+\beta _{17}q^{5}+\cdots\)
476.2.e.c	$476$	$2$	476.e	476.e	$2$	$40$	$40$	$3.801$		None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$