Space of modular forms of level 42, weight 2, and Character 42.d

• Label: 42.2.d
• Level: $42$
• Weight: $2$
• Character orbit: 42.d
• Rep. character: $\chi_{42}(41,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(42, [\chi])\).

	Total	New	Old
Modular forms	12	4	8
Cusp forms	4	4	0
Eisenstein series	8	0	8

Trace form

4 * q - 4 * q^4 - 4 * q^7 - 12 * q^15 + 4 * q^16 + 12 * q^18 + 12 * q^21 + 4 * q^25 + 4 * q^28 - 12 * q^30 - 8 * q^37 - 12 * q^39 - 12 * q^42 + 16 * q^43 - 24 * q^46 - 20 * q^49 + 24 * q^51 + 12 * q^57 + 24 * q^58 + 12 * q^60 - 4 * q^64 + 32 * q^67 + 24 * q^70 - 12 * q^72 + 12 * q^78 - 40 * q^79 - 36 * q^81 - 12 * q^84 - 48 * q^85 + 24 * q^91

Decomposition of \(S_{2}^{\mathrm{new}}(42, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
42.2.d.a	$42$	$2$	42.d	21.c	$2$	$4$	$4$	$0.335$	\(\Q(i, \sqrt{6})\)	None		✓	✓	✓	42.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)