Space of modular forms of level 7, weight 4, and Character 7.c

• Label: 7.4.c
• Level: $7$
• Weight: $4$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(7, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

2 * q - 2 * q^2 - 7 * q^3 + 4 * q^4 - 7 * q^5 + 28 * q^6 + 28 * q^7 - 48 * q^8 - 22 * q^9 - 14 * q^10 + 5 * q^11 + 28 * q^12 - 28 * q^13 + 14 * q^14 + 98 * q^15 + 16 * q^16 + 21 * q^17 - 44 * q^18 - 49 * q^19 - 56 * q^20 - 245 * q^21 - 20 * q^22 + 159 * q^23 + 168 * q^24 + 76 * q^25 + 28 * q^26 - 70 * q^27 + 140 * q^28 + 116 * q^29 - 98 * q^30 - 147 * q^31 - 160 * q^32 + 35 * q^33 - 84 * q^34 + 49 * q^35 - 176 * q^36 - 219 * q^37 - 98 * q^38 + 98 * q^39 + 168 * q^40 + 700 * q^41 + 392 * q^42 - 248 * q^43 - 20 * q^44 - 154 * q^45 + 318 * q^46 - 525 * q^47 - 224 * q^48 + 98 * q^49 - 304 * q^50 + 147 * q^51 - 56 * q^52 - 303 * q^53 + 70 * q^54 - 70 * q^55 - 672 * q^56 + 686 * q^57 - 116 * q^58 + 105 * q^59 + 196 * q^60 + 413 * q^61 + 588 * q^62 + 154 * q^63 + 896 * q^64 + 98 * q^65 + 70 * q^66 - 415 * q^67 - 84 * q^68 - 2226 * q^69 - 490 * q^70 - 864 * q^71 + 528 * q^72 + 1113 * q^73 - 438 * q^74 + 532 * q^75 - 392 * q^76 + 175 * q^77 - 392 * q^78 + 103 * q^79 + 112 * q^80 + 839 * q^81 - 700 * q^82 + 2184 * q^83 - 196 * q^84 - 294 * q^85 + 248 * q^86 - 406 * q^87 - 120 * q^88 + 329 * q^89 + 616 * q^90 - 392 * q^91 + 1272 * q^92 - 1029 * q^93 - 1050 * q^94 - 343 * q^95 - 1120 * q^96 - 1764 * q^97 + 1078 * q^98 - 220 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.4.c.a	$7$	$4$	7.c	7.c	$3$	$2$	$1$	$0.413$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	7.4.c.a	$2$	$0$	\(-2\)	\(-7\)	\(-7\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)