Space of modular forms of level 117, weight 4, and Character 117.l

• Label: 117.4.l
• Level: $117$
• Weight: $4$
• Character orbit: 117.l
• Rep. character: $\chi_{117}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(117, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	80	80	0
Eisenstein series	8	8	0

Trace form

80 * q - q^3 - 306 * q^4 + 42 * q^6 - 3 * q^7 - 17 * q^9 - 10 * q^10 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 63 * q^15 + 1102 * q^16 - 138 * q^17 - 168 * q^18 - 96 * q^19 - 387 * q^20 - 249 * q^21 + 62 * q^22 - 327 * q^23 - 258 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 - 402 * q^29 + 450 * q^30 + 180 * q^31 + 369 * q^33 + 24 * q^34 + 297 * q^35 + 206 * q^36 + 246 * q^37 - 768 * q^38 - 983 * q^39 + 328 * q^40 + 381 * q^41 - 1113 * q^42 - 83 * q^43 - 1038 * q^45 - 6 * q^46 + 372 * q^47 + 1205 * q^48 + 1613 * q^49 - 708 * q^50 + 186 * q^51 + 402 * q^52 - 2568 * q^53 - 627 * q^54 - 127 * q^55 - 2298 * q^56 + 1332 * q^57 + 711 * q^60 - 419 * q^61 + 135 * q^62 + 1845 * q^63 - 3178 * q^64 + 363 * q^65 + 6228 * q^66 + 879 * q^67 + 1950 * q^68 - 3153 * q^69 - 1005 * q^70 - 2598 * q^71 + 1812 * q^72 + 471 * q^74 - 68 * q^75 + 1485 * q^76 - 1584 * q^77 - 60 * q^78 - 260 * q^79 - 1332 * q^80 + 1639 * q^81 - 1273 * q^82 + 1194 * q^83 + 1671 * q^84 - 2910 * q^86 - 1629 * q^87 - 1562 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 - 75 * q^93 + 539 * q^94 + 10584 * q^95 + 6777 * q^96 + 789 * q^97 - 6339 * q^98 - 2331 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(117, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.4.l.a	$117$	$4$	117.l	117.l	$6$	$80$	$40$	$6.903$		None		✓	✓	✓	117.4.l.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{6}]$