Space of modular forms of level 12, weight 13, and Character 12.c

• Label: 12.13.c
• Level: $12$
• Weight: $13$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $26$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
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:			\(26\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(12, [\chi])\).

	Total	New	Old
Modular forms	27	4	23
Cusp forms	21	4	17
Eisenstein series	6	0	6

Trace form

\( 4 q + 300 q^{3} + 15800 q^{7} + 96804 q^{9} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(12, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.13.c.a	$12$	$13$	12.c	3.b	$2$	$4$	$4$	$10.968$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(300\)	\(0\)	\(15800\)	$2^{10}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(75+\beta _{1})q^{3}+(-3\beta _{1}+\beta _{2})q^{5}+(3950+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{13}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{13}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)