Space of modular forms of level 1656, weight 2, and Character 1656.j

• Label: 1656.2.j
• Level: $1656$
• Weight: $2$
• Character orbit: 1656.j
• Rep. character: $\chi_{1656}(323,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1656.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1656, [\chi])\).

	Total	New	Old
Modular forms	296	88	208
Cusp forms	280	88	192
Eisenstein series	16	0	16

Trace form

\( 88 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1656, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1656.2.j.a	$1656$	$2$	1656.j	24.f	$2$	$44$	$44$	$13.223$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1656.2.j.b	$1656$	$2$	1656.j	24.f	$2$	$44$	$44$	$13.223$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)