Space of modular forms of level 117 and weight 6

• Label: 117.6
• Level: 117
• Weight: 6
• Dimension: 1923
• Nonzero newspaces: 15
• Sturm bound: 6048
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 15 \)
Sturm bound:			\(6048\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(117))\).

	Total	New	Old
Modular forms	2616	2021	595
Cusp forms	2424	1923	501
Eisenstein series	192	98	94

Trace form

1923 * q - 36 * q^2 + 72 * q^4 - 162 * q^5 - 366 * q^6 - 292 * q^7 + 2394 * q^8 + 804 * q^9 - 42 * q^10 - 2568 * q^11 - 5472 * q^12 - 2046 * q^13 - 2868 * q^14 + 4080 * q^15 + 7952 * q^16 + 9261 * q^17 + 16176 * q^18 + 4142 * q^19 - 7842 * q^20 - 17364 * q^21 - 7938 * q^22 - 22614 * q^23 - 738 * q^24 + 87 * q^25 + 3072 * q^26 + 20256 * q^27 + 57228 * q^28 + 2427 * q^29 - 80904 * q^30 - 48180 * q^31 - 98862 * q^32 - 9780 * q^33 - 12444 * q^34 + 55740 * q^35 + 113634 * q^36 + 69633 * q^37 + 184914 * q^38 + 59196 * q^39 + 137700 * q^40 + 43905 * q^41 - 19932 * q^42 + 35288 * q^43 - 258540 * q^44 - 217440 * q^45 - 248154 * q^46 - 185412 * q^47 - 36126 * q^48 - 99550 * q^49 + 108030 * q^50 + 146088 * q^51 + 124854 * q^52 - 31776 * q^53 - 16386 * q^54 + 116208 * q^55 + 277740 * q^56 + 208572 * q^57 + 214818 * q^58 + 55428 * q^59 - 139140 * q^60 + 4377 * q^61 + 153534 * q^62 - 10704 * q^63 - 182904 * q^64 - 509481 * q^65 - 393372 * q^66 - 558394 * q^67 - 1068750 * q^68 - 64212 * q^69 - 616860 * q^70 - 20526 * q^71 - 7122 * q^72 + 191090 * q^73 + 1257798 * q^74 + 606360 * q^75 + 1346360 * q^76 + 983592 * q^77 + 1152582 * q^78 + 601992 * q^79 + 1360068 * q^80 - 107964 * q^81 + 740886 * q^82 - 158328 * q^83 - 702420 * q^84 - 1107459 * q^85 - 2185206 * q^86 - 533088 * q^87 - 2536062 * q^88 - 310062 * q^89 - 319404 * q^90 - 290392 * q^91 - 800376 * q^92 - 29028 * q^93 + 692322 * q^94 + 1209666 * q^95 + 408492 * q^96 + 329214 * q^97 - 1054326 * q^98 - 606624 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)

We only show spaces with even 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
117.6.a	\(\chi_{117}(1, \cdot)\)	117.6.a.a	1	1
		117.6.a.b	2
		117.6.a.c	2
		117.6.a.d	3
		117.6.a.e	3
		117.6.a.f	4
		117.6.a.g	4
		117.6.a.h	6
117.6.b	\(\chi_{117}(64, \cdot)\)	117.6.b.a	4	1
		117.6.b.b	4
		117.6.b.c	6
		117.6.b.d	6
		117.6.b.e	8
117.6.e	\(\chi_{117}(40, \cdot)\)	117.6.e.a	60	2
		117.6.e.b	60
117.6.f	\(\chi_{117}(61, \cdot)\)	n/a	136	2
117.6.g	\(\chi_{117}(55, \cdot)\)	117.6.g.a	2	2
		117.6.g.b	8
		117.6.g.c	12
		117.6.g.d	14
		117.6.g.e	20
117.6.h	\(\chi_{117}(16, \cdot)\)	n/a	136	2
117.6.i	\(\chi_{117}(8, \cdot)\)	117.6.i.a	44	2
117.6.l	\(\chi_{117}(4, \cdot)\)	n/a	136	2
117.6.q	\(\chi_{117}(10, \cdot)\)	117.6.q.a	2	2
		117.6.q.b	10
		117.6.q.c	10
		117.6.q.d	12
		117.6.q.e	24
117.6.r	\(\chi_{117}(43, \cdot)\)	n/a	136	2
117.6.t	\(\chi_{117}(25, \cdot)\)	n/a	136	2
117.6.x	\(\chi_{117}(2, \cdot)\)	n/a	272	4
117.6.z	\(\chi_{117}(5, \cdot)\)	n/a	272	4
117.6.ba	\(\chi_{117}(71, \cdot)\)	117.6.ba.a	96	4
117.6.bc	\(\chi_{117}(20, \cdot)\)	n/a	272	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces

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