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

• Label: 456.2.j
• Level: $456$
• Weight: $2$
• Character orbit: 456.j
• Rep. character: $\chi_{456}(419,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	84	72	12
Cusp forms	76	72	4
Eisenstein series	8	0	8

Trace form

\( 72 q - 6 q^{6} + O(q^{10}) \)

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.j.a	$456$	$2$	456.j	24.f	$2$	$4$	$4$	$3.641$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
456.2.j.b	$456$	$2$	456.j	24.f	$2$	$8$	$8$	$3.641$	8.0.170772624.1	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-\beta _{1}-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
456.2.j.c	$456$	$2$	456.j	24.f	$2$	$12$	$12$	$3.641$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(-\beta _{4}+\beta _{5})q^{4}+\cdots\)
456.2.j.d	$456$	$2$	456.j	24.f	$2$	$24$	$24$	$3.641$		None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
456.2.j.e	$456$	$2$	456.j	24.f	$2$	$24$	$24$	$3.641$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)