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

• Label: 42.3.g
• Level: $42$
• Weight: $3$
• Character orbit: 42.g
• Rep. character: $\chi_{42}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.g (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$7$
Character field:			$\Q(\zeta_{6})$
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	40	4	36
Cusp forms	24	4	20
Eisenstein series	16	0	16

Trace form

4 * q + 6 * q^3 - 4 * q^4 + 12 * q^5 - 10 * q^7 + 6 * q^9 - 24 * q^10 - 12 * q^11 - 12 * q^12 + 24 * q^14 + 24 * q^15 - 8 * q^16 - 48 * q^17 - 42 * q^19 + 24 * q^23 + 22 * q^25 + 96 * q^26 + 40 * q^28 - 24 * q^30 + 102 * q^31 - 36 * q^33 - 108 * q^35 - 24 * q^36 + 22 * q^37 + 24 * q^38 + 6 * q^39 + 48 * q^40 + 24 * q^42 + 28 * q^43 - 24 * q^44 + 36 * q^45 - 72 * q^46 - 132 * q^47 - 2 * q^49 - 192 * q^50 - 48 * q^51 + 12 * q^52 + 120 * q^53 - 48 * q^56 - 84 * q^57 - 96 * q^58 - 24 * q^59 - 24 * q^60 - 72 * q^61 + 30 * q^63 + 32 * q^64 + 180 * q^65 + 110 * q^67 + 96 * q^68 + 96 * q^70 + 312 * q^71 - 66 * q^73 - 48 * q^74 + 66 * q^75 + 120 * q^77 + 192 * q^78 - 10 * q^79 - 48 * q^80 - 18 * q^81 + 48 * q^82 + 60 * q^84 - 288 * q^85 - 24 * q^86 - 72 * q^89 - 222 * q^91 - 96 * q^92 + 102 * q^93 - 24 * q^94 - 132 * q^95 - 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.g.a	$42$	$3$	42.g	7.d	$6$	$4$	$2$	$1.144$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓	✓	✓	42.3.g.a	$2$	$0$	$0$	$6$	$12$	$-10$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$

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

$S_{3}^{\mathrm{old}}(42, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(14, [\chi])$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(21, [\chi])$$^{\oplus 2}$