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

• Label: 456.2.g
• Level: $456$
• Weight: $2$
• Character orbit: 456.g
• Rep. character: $\chi_{456}(229,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	84	36	48
Cusp forms	76	36	40
Eisenstein series	8	0	8

Trace form

\( 36 q + 4 q^{2} - 4 q^{4} + 8 q^{7} + 4 q^{8} - 36 q^{9} + O(q^{10}) \)

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.g.a	$456$	$2$	456.g	8.b	$2$	$18$	$18$	$3.641$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{14}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{13}q^{5}+\cdots\)
456.2.g.b	$456$	$2$	456.g	8.b	$2$	$18$	$18$	$3.641$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(20\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots\)

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

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