Space of modular forms of level 456, weight 2, and Character 456.e

• Label: 456.2.e
• Level: $456$
• Weight: $2$
• Character orbit: 456.e
• Rep. character: $\chi_{456}(379,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(456, [\chi])\).

	Total	New	Old
Modular forms	84	40	44
Cusp forms	76	40	36
Eisenstein series	8	0	8

Trace form

\( 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(456, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
456.2.e.a	$456$	$2$	456.e	152.b	$2$	$40$	$40$	$3.641$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(456, [\chi]) \cong \)