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

• Label: 456.2.f
• Level: $456$
• Weight: $2$
• Character orbit: 456.f
• Rep. character: $\chi_{456}(113,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(29\)

Dimensions

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

	Total	New	Old
Modular forms	88	20	68
Cusp forms	72	20	52
Eisenstein series	16	0	16

Trace form

\( 20 q - 4 q^{7} + 6 q^{9} + O(q^{10}) \)

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.f.a	$456$	$2$	456.f	57.d	$2$	$10$	$10$	$3.641$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)
456.2.f.b	$456$	$2$	456.f	57.d	$2$	$10$	$10$	$3.641$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)

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

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