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

• Label: 1656.2.b
• Level: $1656$
• Weight: $2$
• Character orbit: 1656.b
• Rep. character: $\chi_{1656}(413,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1656.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 552 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	296	96	200
Cusp forms	280	96	184
Eisenstein series	16	0	16

Trace form

\( 96 q - 8 q^{4} + O(q^{10}) \)

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.b.a	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.\(\cdots\).17	\(\Q(\sqrt{-46}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}+\beta _{5}q^{5}-2\beta _{1}q^{8}+\cdots\)
1656.2.b.b	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.\(\cdots\).17	\(\Q(\sqrt{-46}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-\beta _{4}q^{5}-2\beta _{1}q^{8}+\cdots\)
1656.2.b.c	$1656$	$2$	1656.b	552.b	$2$	$80$	$80$	$13.223$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1656, [\chi]) \cong \)