Space of modular forms of level 117 and weight 3

• Label: 117.3
• Level: 117
• Weight: 3
• Dimension: 740
• Nonzero newspaces: 15
• Newform subspaces: 21
• Sturm bound: 3024
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(3024\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(117))\).

	Total	New	Old
Modular forms	1104	840	264
Cusp forms	912	740	172
Eisenstein series	192	100	92

Trace form

740 * q - 12 * q^2 - 18 * q^3 - 16 * q^4 - 30 * q^5 - 42 * q^6 - 4 * q^7 + 18 * q^8 - 6 * q^9 - 6 * q^11 - 36 * q^12 - 34 * q^13 - 72 * q^14 - 24 * q^15 - 120 * q^16 - 24 * q^17 - 24 * q^18 - 82 * q^19 + 42 * q^20 - 12 * q^21 + 66 * q^22 + 102 * q^23 + 18 * q^24 + 14 * q^25 - 48 * q^26 - 156 * q^27 - 416 * q^28 - 558 * q^29 - 444 * q^30 - 320 * q^31 - 930 * q^32 - 222 * q^33 - 468 * q^34 - 408 * q^35 - 198 * q^36 + 4 * q^37 + 30 * q^38 + 48 * q^39 + 456 * q^40 + 450 * q^41 + 264 * q^42 + 326 * q^43 + 1056 * q^44 + 504 * q^45 + 630 * q^46 + 732 * q^47 + 630 * q^48 + 442 * q^49 + 792 * q^50 + 126 * q^51 + 512 * q^52 + 24 * q^53 + 138 * q^54 - 60 * q^55 + 348 * q^56 + 42 * q^57 - 36 * q^58 - 294 * q^59 - 360 * q^60 - 320 * q^61 - 1086 * q^62 - 768 * q^63 - 1636 * q^64 - 1656 * q^65 - 1332 * q^66 - 1000 * q^67 - 2250 * q^68 - 600 * q^69 - 1920 * q^70 - 966 * q^71 - 1074 * q^72 - 1018 * q^73 - 1056 * q^74 - 186 * q^75 - 232 * q^76 - 48 * q^77 + 168 * q^78 + 268 * q^79 + 1224 * q^80 + 522 * q^81 + 1092 * q^82 + 1356 * q^83 + 1164 * q^84 + 1584 * q^85 + 2958 * q^86 + 1404 * q^87 + 2922 * q^88 + 1806 * q^89 + 1896 * q^90 + 1520 * q^91 + 2868 * q^92 + 744 * q^93 + 1842 * q^94 + 1506 * q^95 + 2196 * q^96 - 512 * q^97 + 2238 * q^98 + 1200 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
117.3.c	\(\chi_{117}(53, \cdot)\)	117.3.c.a	8	1
117.3.d	\(\chi_{117}(116, \cdot)\)	117.3.d.a	8	1
117.3.j	\(\chi_{117}(73, \cdot)\)	117.3.j.a	4	2
		117.3.j.b	8
		117.3.j.c	8
117.3.k	\(\chi_{117}(29, \cdot)\)	117.3.k.a	52	2
117.3.m	\(\chi_{117}(23, \cdot)\)	117.3.m.a	52	2
117.3.n	\(\chi_{117}(38, \cdot)\)	117.3.n.a	52	2
117.3.o	\(\chi_{117}(17, \cdot)\)	117.3.o.a	20	2
117.3.p	\(\chi_{117}(35, \cdot)\)	117.3.p.a	20	2
117.3.s	\(\chi_{117}(14, \cdot)\)	117.3.s.a	48	2
117.3.u	\(\chi_{117}(68, \cdot)\)	117.3.u.a	52	2
117.3.v	\(\chi_{117}(95, \cdot)\)	117.3.v.a	52	2
117.3.w	\(\chi_{117}(58, \cdot)\)	117.3.w.a	104	4
117.3.y	\(\chi_{117}(31, \cdot)\)	117.3.y.a	104	4
117.3.bb	\(\chi_{117}(7, \cdot)\)	117.3.bb.a	104	4
117.3.bd	\(\chi_{117}(19, \cdot)\)	117.3.bd.a	4	4
		117.3.bd.b	4
		117.3.bd.c	8
		117.3.bd.d	12
		117.3.bd.e	16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(117)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 1}\)