Space of modular forms of level 117 and weight 2

• Label: 117.2
• Level: 117
• Weight: 2
• Dimension: 345
• Nonzero newspaces: 15
• Newform subspaces: 31
• Sturm bound: 2016
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 31 \)
Sturm bound:			\(2016\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(117))\).

	Total	New	Old
Modular forms	600	443	157
Cusp forms	409	345	64
Eisenstein series	191	98	93

Trace form

345 * q - 18 * q^2 - 24 * q^3 - 18 * q^4 - 18 * q^5 - 24 * q^6 - 20 * q^7 - 27 * q^8 - 24 * q^9 - 69 * q^10 - 24 * q^11 - 24 * q^12 - 30 * q^13 - 48 * q^14 - 24 * q^15 - 38 * q^16 - 27 * q^17 - 24 * q^18 - 74 * q^19 - 51 * q^20 - 24 * q^21 - 48 * q^22 - 30 * q^23 - 39 * q^25 - 48 * q^26 - 48 * q^27 - 72 * q^28 + 3 * q^29 + 24 * q^30 + 12 * q^31 + 60 * q^32 + 12 * q^33 + 30 * q^34 + 60 * q^35 + 72 * q^36 - 15 * q^37 + 108 * q^38 + 24 * q^39 + 84 * q^40 + 33 * q^41 + 48 * q^42 - 8 * q^43 + 96 * q^44 + 36 * q^45 - 42 * q^46 + 12 * q^47 + 48 * q^48 - 20 * q^49 + 33 * q^50 - 69 * q^52 - 84 * q^53 - 24 * q^54 - 120 * q^55 - 36 * q^56 - 24 * q^57 - 93 * q^58 - 60 * q^59 + 36 * q^60 - 75 * q^61 - 30 * q^62 + 24 * q^63 - 33 * q^64 + 45 * q^65 + 72 * q^66 + 22 * q^67 + 171 * q^68 + 48 * q^69 + 132 * q^70 + 114 * q^71 + 132 * q^72 + 70 * q^73 + 195 * q^74 + 96 * q^75 + 130 * q^76 + 108 * q^77 + 204 * q^78 + 291 * q^80 + 72 * q^81 + 75 * q^82 + 144 * q^83 + 144 * q^84 + 81 * q^85 + 168 * q^86 + 72 * q^87 + 96 * q^88 + 30 * q^89 + 132 * q^90 - 56 * q^91 + 60 * q^92 + 48 * q^93 - 18 * q^94 - 30 * q^95 - 180 * q^96 - 78 * q^97 - 42 * q^98 - 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)

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
117.2.a	\(\chi_{117}(1, \cdot)\)	117.2.a.a	1	1
		117.2.a.b	2
		117.2.a.c	2
117.2.b	\(\chi_{117}(64, \cdot)\)	117.2.b.a	2	1
		117.2.b.b	4
117.2.e	\(\chi_{117}(40, \cdot)\)	117.2.e.a	2	2
		117.2.e.b	10
		117.2.e.c	12
117.2.f	\(\chi_{117}(61, \cdot)\)	117.2.f.a	24	2
117.2.g	\(\chi_{117}(55, \cdot)\)	117.2.g.a	2	2
		117.2.g.b	2
		117.2.g.c	4
117.2.h	\(\chi_{117}(16, \cdot)\)	117.2.h.a	24	2
117.2.i	\(\chi_{117}(8, \cdot)\)	117.2.i.a	12	2
117.2.l	\(\chi_{117}(4, \cdot)\)	117.2.l.a	2	2
		117.2.l.b	22
117.2.q	\(\chi_{117}(10, \cdot)\)	117.2.q.a	2	2
		117.2.q.b	2
		117.2.q.c	2
		117.2.q.d	4
117.2.r	\(\chi_{117}(43, \cdot)\)	117.2.r.a	2	2
		117.2.r.b	22
117.2.t	\(\chi_{117}(25, \cdot)\)	117.2.t.a	2	2
		117.2.t.b	2
		117.2.t.c	20
117.2.x	\(\chi_{117}(2, \cdot)\)	117.2.x.a	48	4
117.2.z	\(\chi_{117}(5, \cdot)\)	117.2.z.a	4	4
		117.2.z.b	44
117.2.ba	\(\chi_{117}(71, \cdot)\)	117.2.ba.a	8	4
		117.2.ba.b	8
117.2.bc	\(\chi_{117}(20, \cdot)\)	117.2.bc.a	48	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces

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