Space of modular forms of level 117, weight 3, and Character 117.w

• Label: 117.3.w
• Level: $117$
• Weight: $3$
• Character orbit: 117.w
• Rep. character: $\chi_{117}(58,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $104$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$117 = 3^{2} \cdot 13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	117.w (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$117$
Character field:			$\Q(\zeta_{12})$
Newform subspaces:			$1$
Sturm bound:			$42$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(117, [\chi])$.

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

104 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 - 32 * q^6 + 18 * q^8 - 2 * q^9 - 12 * q^10 + 22 * q^11 + 54 * q^12 - 2 * q^13 - 4 * q^14 + 70 * q^15 - 324 * q^16 - 12 * q^17 - 86 * q^18 - 36 * q^19 + 134 * q^20 - 32 * q^21 - 4 * q^22 - 6 * q^23 + 30 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 - 148 * q^29 - 246 * q^30 + 62 * q^31 + 70 * q^32 + 52 * q^33 - 18 * q^34 - 106 * q^35 + 96 * q^36 + 14 * q^37 + 216 * q^38 + 118 * q^39 - 36 * q^40 - 26 * q^41 + 278 * q^42 - 198 * q^43 + 496 * q^44 - 80 * q^45 - 8 * q^47 + 58 * q^48 - 6 * q^49 - 292 * q^50 + 28 * q^52 - 208 * q^53 + 58 * q^54 - 4 * q^55 + 186 * q^56 - 140 * q^57 + 146 * q^58 - 434 * q^59 + 140 * q^60 + 2 * q^61 - 282 * q^62 - 266 * q^63 - 260 * q^65 - 412 * q^66 + 138 * q^67 + 534 * q^68 - 294 * q^69 + 212 * q^70 - 8 * q^71 - 306 * q^72 + 90 * q^73 - 178 * q^74 - 60 * q^75 - 98 * q^76 - 432 * q^77 + 352 * q^78 - 16 * q^79 - 278 * q^80 - 230 * q^81 - 12 * q^82 - 50 * q^83 + 1066 * q^84 + 204 * q^85 + 330 * q^86 - 154 * q^87 + 400 * q^89 - 798 * q^90 + 120 * q^91 + 48 * q^92 - 128 * q^93 + 122 * q^94 + 958 * q^96 - 232 * q^97 + 280 * q^98 + 940 * q^99

Decomposition of $S_{3}^{\mathrm{new}}(117, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.3.w.a	$117$	$3$	117.w	117.w	$12$	$104$	$26$	$3.188$		None		✓	✓	✓	117.3.w.a	$2$	$0$	$-2$	$-2$	$-2$	$0$		$\mathrm{SU}(2)[C_{12}]$