Space of modular forms of level 116 and weight 2

• Label: 116.2
• Level: 116
• Weight: 2
• Dimension: 217
• Nonzero newspaces: 6
• Newform subspaces: 13
• Sturm bound: 1680
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1680\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(116))\).

	Total	New	Old
Modular forms	490	273	217
Cusp forms	351	217	134
Eisenstein series	139	56	83

Trace form

217 * q - 14 * q^2 - 14 * q^4 - 28 * q^5 - 14 * q^6 - 14 * q^8 - 28 * q^9 - 14 * q^10 - 14 * q^12 - 28 * q^13 - 14 * q^14 - 14 * q^16 - 28 * q^17 - 14 * q^18 - 14 * q^20 - 56 * q^21 - 14 * q^22 - 14 * q^23 - 14 * q^24 - 56 * q^25 - 14 * q^26 - 42 * q^27 - 56 * q^29 - 28 * q^30 - 28 * q^31 - 14 * q^32 - 70 * q^33 - 14 * q^34 - 28 * q^35 - 14 * q^36 - 42 * q^37 - 14 * q^38 - 28 * q^39 - 14 * q^40 - 28 * q^41 - 14 * q^42 + 7 * q^45 + 56 * q^46 + 28 * q^47 + 98 * q^48 + 28 * q^49 + 84 * q^50 + 56 * q^51 + 98 * q^52 + 35 * q^53 + 112 * q^54 + 112 * q^55 + 84 * q^56 + 56 * q^57 + 154 * q^58 + 28 * q^59 + 154 * q^60 + 28 * q^61 + 84 * q^62 + 112 * q^63 + 112 * q^64 + 35 * q^65 + 98 * q^66 + 56 * q^67 + 84 * q^68 + 28 * q^69 + 98 * q^70 - 14 * q^71 + 56 * q^72 - 21 * q^73 - 70 * q^75 - 14 * q^76 - 98 * q^77 - 14 * q^78 - 28 * q^79 - 14 * q^80 - 140 * q^81 - 14 * q^82 - 56 * q^83 - 56 * q^84 - 112 * q^85 - 70 * q^87 - 28 * q^88 - 98 * q^89 + 28 * q^90 - 84 * q^91 - 14 * q^92 - 84 * q^93 - 14 * q^94 - 112 * q^95 - 56 * q^96 + 21 * q^97 - 84 * q^98 - 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)

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
116.2.a	\(\chi_{116}(1, \cdot)\)	116.2.a.a	1	1
		116.2.a.b	1
		116.2.a.c	1
116.2.c	\(\chi_{116}(57, \cdot)\)	116.2.c.a	2	1
116.2.e	\(\chi_{116}(75, \cdot)\)	116.2.e.a	2	2
		116.2.e.b	4
		116.2.e.c	20
116.2.g	\(\chi_{116}(25, \cdot)\)	116.2.g.a	6	6
		116.2.g.b	12
116.2.i	\(\chi_{116}(5, \cdot)\)	116.2.i.a	6	6
		116.2.i.b	6
116.2.l	\(\chi_{116}(3, \cdot)\)	116.2.l.a	12	12
		116.2.l.b	144

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)