Space of modular forms of level 12, weight 7, and Character 12.c

• Label: 12.7.c
• Level: $12$
• Weight: $7$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(12, [\chi])\).

	Total	New	Old
Modular forms	15	2	13
Cusp forms	9	2	7
Eisenstein series	6	0	6

Trace form

\( 2 q - 6 q^{3} + 484 q^{7} - 1422 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(12, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.7.c.a	$12$	$7$	12.c	3.b	$2$	$2$	$2$	$2.761$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(484\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)