Space of modular forms of level 42, weight 3, and Character 42.c

• Label: 42.3.c
• Level: $42$
• Weight: $3$
• Character orbit: 42.c
• Rep. character: $\chi_{42}(13,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	42.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(42, [\chi])\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	12	4	8
Eisenstein series	8	0	8

Trace form

4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 - 24 * q^15 + 16 * q^16 + 12 * q^21 - 24 * q^22 + 24 * q^23 + 28 * q^25 + 16 * q^28 + 120 * q^29 + 24 * q^30 - 24 * q^35 - 24 * q^36 - 80 * q^37 + 96 * q^39 + 48 * q^42 - 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 + 96 * q^50 - 24 * q^51 - 216 * q^53 - 48 * q^56 - 24 * q^57 - 48 * q^60 - 24 * q^63 + 32 * q^64 + 240 * q^65 + 176 * q^67 + 72 * q^70 - 120 * q^71 + 288 * q^74 + 24 * q^77 - 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 + 216 * q^85 - 240 * q^86 - 48 * q^88 + 48 * q^92 - 144 * q^93 - 240 * q^95 - 192 * q^98 + 72 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(42, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
42.3.c.a	$42$	$3$	42.c	7.b	$2$	$4$	$4$	$1.144$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓	✓	42.3.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(42, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)