Space of modular forms of level 42, weight 12, and Character 42.d

• Label: 42.12.d
• Level: $42$
• Weight: $12$
• Character orbit: 42.d
• Rep. character: $\chi_{42}(41,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(42, [\chi])\).

	Total	New	Old
Modular forms	92	28	64
Cusp forms	84	28	56
Eisenstein series	8	0	8

Trace form

\( 28 q - 28672 q^{4} - 23884 q^{7} + 9600 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(42, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
42.12.d.a	$42$	$12$	42.d	21.c	$2$	$28$	$28$	$32.270$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-23884\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{12}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)