Space of modular forms of level 7, weight 8, and Character 7.c

• Label: 7.8.c
• Level: $7$
• Weight: $8$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(7, [\chi])\).

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

Trace form

8 * q + 6 * q^2 - 28 * q^3 - 348 * q^4 - 252 * q^5 + 2044 * q^6 + 672 * q^7 - 1968 * q^8 - 2008 * q^9 - 4774 * q^10 + 3972 * q^11 + 5404 * q^12 - 2352 * q^13 + 47502 * q^14 - 33112 * q^15 - 57264 * q^16 - 56364 * q^17 + 35908 * q^18 - 41748 * q^19 + 324744 * q^20 + 188524 * q^21 - 305908 * q^22 - 131748 * q^23 - 389592 * q^24 + 68016 * q^25 - 113652 * q^26 + 378056 * q^27 + 681548 * q^28 + 68112 * q^29 - 605378 * q^30 - 401212 * q^31 + 453408 * q^32 - 24052 * q^33 + 164220 * q^34 + 40404 * q^35 - 720176 * q^36 + 5396 * q^37 - 31794 * q^38 - 364840 * q^39 + 443688 * q^40 + 820848 * q^41 - 240856 * q^42 + 93088 * q^43 + 1465836 * q^44 + 1209656 * q^45 - 1379202 * q^46 - 1470084 * q^47 - 4037600 * q^48 - 2793784 * q^49 + 2791056 * q^50 + 1724796 * q^51 + 5269768 * q^52 + 642372 * q^53 + 4567318 * q^54 - 6126680 * q^55 - 6195168 * q^56 + 6718136 * q^57 + 1972220 * q^58 - 752220 * q^59 - 2123324 * q^60 - 1325772 * q^61 - 6032628 * q^62 - 6412616 * q^63 - 1731712 * q^64 + 4868808 * q^65 + 6013294 * q^66 + 290916 * q^67 - 2453556 * q^68 + 9830520 * q^69 + 11665990 * q^70 + 6755520 * q^71 - 4557744 * q^72 - 6706588 * q^73 - 3616878 * q^74 - 7223888 * q^75 + 5846008 * q^76 - 5310564 * q^77 - 32576264 * q^78 - 3946244 * q^79 - 10695888 * q^80 + 11731292 * q^81 + 17563252 * q^82 + 19084128 * q^83 + 38088092 * q^84 + 14012136 * q^85 - 23237832 * q^86 - 17836840 * q^87 + 8043336 * q^88 - 16165212 * q^89 + 6831496 * q^90 - 2414720 * q^91 - 38885256 * q^92 - 12552852 * q^93 - 5720442 * q^94 + 3268452 * q^95 + 8448608 * q^96 + 3066224 * q^97 + 60255006 * q^98 + 30427952 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.8.c.a	$7$	$8$	7.c	7.c	$3$	$8$	$4$	$2.187$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	7.8.c.a	$2$	$0$	\(6\)	\(-28\)	\(-252\)	\(672\)	$2^{8}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(-6+\cdots)q^{3}+\cdots\)