Space of modular forms of level 12, weight 7, and Character 12.d

• Label: 12.7.d
• Level: $12$
• Weight: $7$
• Character orbit: 12.d
• Rep. character: $\chi_{12}(7,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(12, [\chi])\).

	Total	New	Old
Modular forms	14	6	8
Cusp forms	10	6	4
Eisenstein series	4	0	4

Trace form

6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Decomposition of \(S_{7}^{\mathrm{new}}(12, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.7.d.a	$12$	$7$	12.d	4.b	$2$	$6$	$6$	$2.761$	6.0.50898483.1	None		✓	✓	✓	12.7.d.a	$2$	$0$	\(-10\)	\(0\)	\(-44\)	\(0\)	$2^{12}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{1})q^{2}-\beta _{2}q^{3}+(3^{3}+2\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(12, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)