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 - 2225148 * q^15 + 29360128 * q^16 + 8028288 * q^18 - 38450580 * q^21 + 24372480 * q^22 + 163501900 * q^25 + 24457216 * q^28 - 544245888 * q^30 - 9830400 * q^36 + 2357964952 * q^37 + 353730228 * q^39 + 362022528 * q^42 - 4118873216 * q^43 + 25399296 * q^46 - 6877051916 * q^49 + 12890051400 * q^51 - 3380443548 * q^57 + 15400348416 * q^58 + 2278551552 * q^60 - 2899758120 * q^63 - 30064771072 * q^64 + 56654396432 * q^67 - 51033249792 * q^70 - 8220966912 * q^72 - 42658776192 * q^78 + 241379531528 * q^79 - 30629202588 * q^81 + 39373393920 * q^84 - 304984462176 * q^85 - 24957419520 * q^88 - 123715256616 * q^91 - 374931920160 * q^93 + 554680171584 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	42.12.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-23884\)		$\mathrm{SU}(2)[C_{2}]$

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

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