Space of modular forms of level 7, weight 7, and Character 7.b

• Label: 7.7.b
• Level: $7$
• Weight: $7$
• Character orbit: 7.b
• Rep. character: $\chi_{7}(6,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $4$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(4\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

Trace form

\( 3 q - 7 q^{2} + 17 q^{4} - 77 q^{7} + 601 q^{8} - 1893 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(7, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.7.b.a	$7$	$7$	7.b	7.b	$2$	$1$	$1$	$1.610$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(9\)	\(0\)	\(0\)	\(-343\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
7.7.b.b	$7$	$7$	7.b	7.b	$2$	$2$	$2$	$1.610$	\(\Q(\sqrt{-510}) \)	None		$2$	$0$	\(-16\)	\(0\)	\(0\)	\(266\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)