Space of modular forms of level 56, weight 7, and Character 56.k

• Label: 56.7.k
• Level: $56$
• Weight: $7$
• Character orbit: 56.k
• Rep. character: $\chi_{56}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	56.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(56, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

\( 92 q + 4 q^{2} - 2 q^{3} + 44 q^{4} + 124 q^{6} + 1132 q^{8} - 10208 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(56, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
56.7.k.a	$56$	$7$	56.k	56.k	$6$	$92$	$46$	$12.883$		None		$4$	$0$	\(4\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$