Space of modular forms of level 114 and weight 2

• Label: 114.2
• Level: 114
• Weight: 2
• Dimension: 91
• Nonzero newspaces: 6
• Newform subspaces: 21
• Sturm bound: 1440
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1440\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(114))\).

	Total	New	Old
Modular forms	432	91	341
Cusp forms	289	91	198
Eisenstein series	143	0	143

Trace form

91 * q + q^2 + q^3 + q^4 + 6 * q^5 + q^6 + 8 * q^7 + q^8 + q^9 + 6 * q^10 + 12 * q^11 - 5 * q^12 - 34 * q^13 - 28 * q^14 - 30 * q^15 + q^16 - 18 * q^17 + q^18 - 65 * q^19 - 30 * q^20 - 34 * q^21 - 42 * q^22 - 12 * q^23 + q^24 - 41 * q^25 - 22 * q^26 - 14 * q^27 - 4 * q^28 - 6 * q^29 + 6 * q^30 - 4 * q^31 + q^32 - 42 * q^33 + 18 * q^34 - 24 * q^35 + q^36 + 2 * q^37 + 19 * q^38 - 40 * q^39 + 6 * q^40 + 6 * q^41 + 8 * q^42 - 28 * q^43 + 12 * q^44 + 6 * q^45 + 24 * q^46 + 12 * q^47 + 10 * q^48 + 21 * q^49 + 31 * q^50 + 99 * q^51 + 14 * q^52 + 54 * q^53 + 55 * q^54 + 72 * q^55 + 8 * q^56 + 109 * q^57 + 30 * q^58 + 60 * q^59 + 42 * q^60 + 50 * q^61 + 32 * q^62 + 74 * q^63 + q^64 + 48 * q^65 + 84 * q^66 - 4 * q^67 + 18 * q^68 + 78 * q^69 + 48 * q^70 + 36 * q^71 + 10 * q^72 + 20 * q^73 + 38 * q^74 - 11 * q^75 + 19 * q^76 + 24 * q^77 - 22 * q^78 - 76 * q^79 + 6 * q^80 - 71 * q^81 - 30 * q^82 - 60 * q^83 - 46 * q^84 - 36 * q^85 - 28 * q^86 - 150 * q^87 + 12 * q^88 - 54 * q^89 - 84 * q^90 - 80 * q^91 - 48 * q^92 - 118 * q^93 - 96 * q^94 + 6 * q^95 + q^96 - 10 * q^97 - 87 * q^98 - 69 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.2.a	\(\chi_{114}(1, \cdot)\)	114.2.a.a	1	1
		114.2.a.b	1
		114.2.a.c	1
114.2.b	\(\chi_{114}(113, \cdot)\)	114.2.b.a	2	1
		114.2.b.b	2
		114.2.b.c	2
		114.2.b.d	2
114.2.e	\(\chi_{114}(7, \cdot)\)	114.2.e.a	2	2
		114.2.e.b	2
114.2.h	\(\chi_{114}(65, \cdot)\)	114.2.h.a	2	2
		114.2.h.b	2
		114.2.h.c	2
		114.2.h.d	2
		114.2.h.e	4
		114.2.h.f	4
114.2.i	\(\chi_{114}(25, \cdot)\)	114.2.i.a	6	6
		114.2.i.b	6
		114.2.i.c	6
		114.2.i.d	6
114.2.l	\(\chi_{114}(29, \cdot)\)	114.2.l.a	18	6
		114.2.l.b	18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(114)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)