Space of modular forms of level 3, weight 7, and Character 3.b

• Label: 3.7.b
• Level: $3$
• Weight: $7$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(3, [\chi])\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	1	1	0
Eisenstein series	2	2	0

Trace form

\( q - 27 q^{3} + 64 q^{4} - 286 q^{7} + 729 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(3, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.7.b.a	$3$	$7$	3.b	3.b	$2$	$1$	$1$	$0.690$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-27\)	\(0\)	\(-286\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)