Space of modular forms of level 1656, weight 4, and Character 1656.m

• Label: 1656.4.m
• Level: $1656$
• Weight: $4$
• Character orbit: 1656.m
• Rep. character: $\chi_{1656}(1241,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $1152$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1656.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1152\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1656, [\chi])\).

	Total	New	Old
Modular forms	880	72	808
Cusp forms	848	72	776
Eisenstein series	32	0	32

Trace form

\( 72 q + 1656 q^{25} + 432 q^{31} - 3768 q^{49} + 1152 q^{55} + 768 q^{73} - 6960 q^{85}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1656, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1656.4.m.a	$1656$	$4$	1656.m	69.c	$2$	$72$	$72$	$97.707$		None		✓	✓	✓	1656.4.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1656, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1656, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(828, [\chi])\)\(^{\oplus 2}\)