Space of modular forms of level 7, weight 26, and Character 7.c

• Label: 7.26.c
• Level: $7$
• Weight: $26$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $17$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(17\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(7, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	32	32	0
Eisenstein series	4	4	0

Trace form

\( 32 q - 4050 q^{2} + 531440 q^{3} - 286295596 q^{4} + 288173088 q^{5} - 13063290884 q^{6} - 55218840880 q^{7} + 274366746720 q^{8} - 5146896583216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(7, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.26.c.a	$7$	$26$	7.c	7.c	$3$	$32$	$16$	$27.720$		None		$2$	$0$	\(-4050\)	\(531440\)	\(288173088\)	\(-55218840880\)		$\mathrm{SU}(2)[C_{3}]$