Space of modular forms of level 7, weight 6, and Character 7.c

• Label: 7.6.c
• Level: $7$
• Weight: $6$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(7, [\chi])\).

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

Trace form

4 * q - 2 * q^2 + 8 * q^3 - 12 * q^4 + 38 * q^5 - 164 * q^6 - 168 * q^7 + 192 * q^8 + 380 * q^9 + 778 * q^10 - 424 * q^11 + 196 * q^12 - 1848 * q^13 - 2674 * q^14 + 1784 * q^15 + 2064 * q^16 + 2346 * q^17 - 212 * q^18 + 360 * q^19 - 3416 * q^20 - 1526 * q^21 + 4252 * q^22 + 12 * q^23 - 1392 * q^24 - 1872 * q^25 - 1148 * q^26 + 5744 * q^27 + 2548 * q^28 - 14104 * q^29 - 5258 * q^30 - 3548 * q^31 + 8096 * q^32 + 3398 * q^33 + 14844 * q^34 + 27496 * q^35 - 2192 * q^36 - 11090 * q^37 - 20138 * q^38 - 1624 * q^39 - 15936 * q^40 + 7000 * q^41 - 3472 * q^42 - 25360 * q^43 - 5948 * q^44 - 1300 * q^45 + 5118 * q^46 + 22956 * q^47 + 22432 * q^48 + 4900 * q^49 + 59984 * q^50 + 384 * q^51 + 1400 * q^52 - 3042 * q^53 - 32546 * q^54 - 50152 * q^55 - 57792 * q^56 - 38116 * q^57 + 58852 * q^58 + 65808 * q^59 - 14084 * q^60 + 42486 * q^61 - 98724 * q^62 - 4760 * q^63 + 70912 * q^64 + 3164 * q^65 + 25894 * q^66 - 42312 * q^67 - 5460 * q^68 + 10308 * q^69 - 113050 * q^70 - 4416 * q^71 + 32448 * q^72 + 50506 * q^73 + 47370 * q^74 + 35608 * q^75 + 77672 * q^76 + 65338 * q^77 + 55048 * q^78 - 9004 * q^79 - 68816 * q^80 - 51178 * q^81 - 67732 * q^82 - 208656 * q^83 + 44492 * q^84 - 106212 * q^85 - 86776 * q^86 - 80008 * q^87 + 20496 * q^88 + 26666 * q^89 + 261304 * q^90 + 135632 * q^91 - 20568 * q^92 - 38718 * q^93 - 98034 * q^94 + 198140 * q^95 - 54880 * q^96 + 418264 * q^97 + 98686 * q^98 - 133888 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.6.c.a	$7$	$6$	7.c	7.c	$3$	$4$	$2$	$1.123$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		✓	✓	✓	7.6.c.a	$2$	$0$	\(-2\)	\(8\)	\(38\)	\(-168\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)