Space of modular forms of level 1264 and weight 1

• Label: 1264.1
• Level: 1264
• Weight: 1
• Dimension: 20
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 99840
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(99840\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1264))\).

	Total	New	Old
Modular forms	1140	367	773
Cusp forms	48	20	28
Eisenstein series	1092	347	745

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	8	0

Trace form

20 * q + 2 * q^2 - q^5 + 4 * q^7 - 4 * q^8 + 2 * q^9 + 3 * q^11 + 8 * q^12 + q^13 + 4 * q^14 - 4 * q^16 - 4 * q^18 + 3 * q^19 - 4 * q^22 + q^23 + 4 * q^24 + q^25 + 12 * q^26 - 2 * q^29 + q^31 - 8 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 4 * q^38 - 4 * q^39 + 10 * q^40 - 2 * q^44 - q^45 + 4 * q^46 - 8 * q^49 - 12 * q^50 - 4 * q^51 + 4 * q^52 - 2 * q^53 + 2 * q^55 - 2 * q^56 + 4 * q^58 + 2 * q^59 - 4 * q^61 - 2 * q^65 + q^67 - 4 * q^68 - 8 * q^69 - 8 * q^71 - 2 * q^72 - q^73 - 2 * q^74 - 2 * q^76 - 2 * q^77 - 12 * q^79 - 12 * q^81 + 2 * q^82 - 14 * q^83 + 4 * q^84 - 8 * q^87 - 2 * q^88 - q^89 + 4 * q^91 + 4 * q^92 - 8 * q^94 - 3 * q^95 - q^97 + 3 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1264))\)

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
1264.1.d	\(\chi_{1264}(159, \cdot)\)	None	0	1
1264.1.e	\(\chi_{1264}(1105, \cdot)\)	1264.1.e.a	2	1
1264.1.f	\(\chi_{1264}(473, \cdot)\)	None	0	1
1264.1.g	\(\chi_{1264}(791, \cdot)\)	None	0	1
1264.1.l	\(\chi_{1264}(157, \cdot)\)	1264.1.l.a	2	2
		1264.1.l.b	8
1264.1.m	\(\chi_{1264}(475, \cdot)\)	None	0	2
1264.1.o	\(\chi_{1264}(23, \cdot)\)	None	0	2
1264.1.p	\(\chi_{1264}(1209, \cdot)\)	None	0	2
1264.1.q	\(\chi_{1264}(577, \cdot)\)	None	0	2
1264.1.r	\(\chi_{1264}(655, \cdot)\)	None	0	2
1264.1.u	\(\chi_{1264}(261, \cdot)\)	None	0	4
1264.1.v	\(\chi_{1264}(339, \cdot)\)	1264.1.v.a	4	4
		1264.1.v.b	4
1264.1.ba	\(\chi_{1264}(87, \cdot)\)	None	0	12
1264.1.bb	\(\chi_{1264}(41, \cdot)\)	None	0	12
1264.1.bc	\(\chi_{1264}(17, \cdot)\)	None	0	12
1264.1.bd	\(\chi_{1264}(143, \cdot)\)	None	0	12
1264.1.bh	\(\chi_{1264}(67, \cdot)\)	None	0	24
1264.1.bi	\(\chi_{1264}(61, \cdot)\)	None	0	24
1264.1.bn	\(\chi_{1264}(31, \cdot)\)	None	0	24
1264.1.bo	\(\chi_{1264}(113, \cdot)\)	None	0	24
1264.1.bp	\(\chi_{1264}(153, \cdot)\)	None	0	24
1264.1.bq	\(\chi_{1264}(119, \cdot)\)	None	0	24
1264.1.bu	\(\chi_{1264}(11, \cdot)\)	None	0	48
1264.1.bv	\(\chi_{1264}(29, \cdot)\)	None	0	48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1264))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1264)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(316))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(632))\)\(^{\oplus 2}\)