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Properties

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

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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

\( 20 q + 2 q^{2} - q^{5} + 4 q^{7} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{2} - q^{5} + 4 q^{7} - 4 q^{8} + 2 q^{9} + 3 q^{11} + 8 q^{12} + q^{13} + 4 q^{14} - 4 q^{16} - 4 q^{18} + 3 q^{19} - 4 q^{22} + q^{23} + 4 q^{24} + q^{25} + 12 q^{26} - 2 q^{29} + q^{31} - 8 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 4 q^{38} - 4 q^{39} + 10 q^{40} - 2 q^{44} - q^{45} + 4 q^{46} - 8 q^{49} - 12 q^{50} - 4 q^{51} + 4 q^{52} - 2 q^{53} + 2 q^{55} - 2 q^{56} + 4 q^{58} + 2 q^{59} - 4 q^{61} - 2 q^{65} + q^{67} - 4 q^{68} - 8 q^{69} - 8 q^{71} - 2 q^{72} - q^{73} - 2 q^{74} - 2 q^{76} - 2 q^{77} - 12 q^{79} - 12 q^{81} + 2 q^{82} - 14 q^{83} + 4 q^{84} - 8 q^{87} - 2 q^{88} - q^{89} + 4 q^{91} + 4 q^{92} - 8 q^{94} - 3 q^{95} - q^{97} + 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{1}^{\mathrm{old}}(\Gamma_1(1264)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(632))\)\(^{\oplus 2}\)