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

• Label: 7.12.c
• Level: $7$
• Weight: $12$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

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

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

Trace form

12 * q + 22 * q^2 - 244 * q^3 - 2556 * q^4 - 8782 * q^5 + 38140 * q^6 - 504 * q^7 + 97008 * q^8 - 172348 * q^9 + 111546 * q^10 - 1001572 * q^11 - 173684 * q^12 + 3864504 * q^13 - 1302994 * q^14 - 1286512 * q^15 + 39120 * q^16 - 6704802 * q^17 + 3768052 * q^18 + 4192212 * q^19 - 17646776 * q^20 + 44745358 * q^21 - 8505684 * q^22 - 33871872 * q^23 - 15734760 * q^24 + 13695456 * q^25 + 29350300 * q^26 + 73859384 * q^27 + 181285692 * q^28 - 255125224 * q^29 - 336068498 * q^30 - 331783920 * q^31 + 163252640 * q^32 - 80899438 * q^33 + 1853334396 * q^34 + 1407354844 * q^35 - 2197352048 * q^36 - 833082774 * q^37 - 2086458338 * q^38 + 737605904 * q^39 - 1219023432 * q^40 + 3104076808 * q^41 + 5982095000 * q^42 - 1722177552 * q^43 - 5105122436 * q^44 - 7406493484 * q^45 + 3435559326 * q^46 - 1327587552 * q^47 + 14535793696 * q^48 + 11976558636 * q^49 - 12237094384 * q^50 - 13921261140 * q^51 - 17237001432 * q^52 + 6725755626 * q^53 - 1674595226 * q^54 + 26323921200 * q^55 + 28163516640 * q^56 - 16884487756 * q^57 - 20073189204 * q^58 - 26237179548 * q^59 + 13611677716 * q^60 - 14411013726 * q^61 + 46185665964 * q^62 + 45955779184 * q^63 - 46365999744 * q^64 - 16224702172 * q^65 - 40938633602 * q^66 - 4241860068 * q^67 - 6528332916 * q^68 + 46750854252 * q^69 + 55705143270 * q^70 - 37335334656 * q^71 - 30237166608 * q^72 + 6005568990 * q^73 + 21663581922 * q^74 + 17116276792 * q^75 - 28817353320 * q^76 - 51928077698 * q^77 + 42636498520 * q^78 + 11712395640 * q^79 + 41748525232 * q^80 - 12455008366 * q^81 + 52795921668 * q^82 - 100821781200 * q^83 - 155783007940 * q^84 + 138884613396 * q^85 + 110437384472 * q^86 + 119455310144 * q^87 - 105039956616 * q^88 - 48633519778 * q^89 - 361508123864 * q^90 - 160908361488 * q^91 + 242956324248 * q^92 + 266530114134 * q^93 + 368497095702 * q^94 - 72161225128 * q^95 + 124456168928 * q^96 - 401308415928 * q^97 - 582375436706 * q^98 + 367357472240 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.12.c.a	$7$	$12$	7.c	7.c	$3$	$12$	$6$	$5.378$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	7.12.c.a	$2$	$0$	\(22\)	\(-244\)	\(-8782\)	\(-504\)	$2^{20}\cdot 3^{3}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)