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Properties

Label 2564.1
Level 2564
Weight 1
Dimension 171
Nonzero newspaces 11
Newform subspaces 14
Sturm bound 410880
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2564 = 2^{2} \cdot 641 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 14 \)
Sturm bound: \(410880\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2564))\).

Total New Old
Modular forms 1771 809 962
Cusp forms 171 171 0
Eisenstein series 1600 638 962

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 171 0 0 0

Trace form

\( 171 q - q^{2} + 11 q^{4} - 2 q^{5} - q^{8} + 11 q^{9} + O(q^{10}) \) \( 171 q - q^{2} + 11 q^{4} - 2 q^{5} - q^{8} + 11 q^{9} - 6 q^{10} - 2 q^{13} + 11 q^{16} - 2 q^{17} - 5 q^{18} - 2 q^{20} + 5 q^{25} - 6 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} + 11 q^{36} - 6 q^{37} - 6 q^{40} - 2 q^{41} - 10 q^{45} + 11 q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} - 4 q^{57} - 2 q^{58} - 2 q^{61} + 11 q^{64} - 12 q^{65} - 2 q^{68} - 4 q^{69} - 5 q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{85} - 6 q^{89} - 6 q^{90} - 4 q^{93} - 2 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2564))\)

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
2564.1.b \(\chi_{2564}(1283, \cdot)\) None 0 1
2564.1.d \(\chi_{2564}(2563, \cdot)\) 2564.1.d.a 1 1
2564.1.d.b 3
2564.1.d.c 3
2564.1.d.d 6
2564.1.f \(\chi_{2564}(487, \cdot)\) 2564.1.f.a 2 2
2564.1.i \(\chi_{2564}(323, \cdot)\) 2564.1.i.a 4 4
2564.1.j \(\chi_{2564}(79, \cdot)\) 2564.1.j.a 4 4
2564.1.l \(\chi_{2564}(531, \cdot)\) 2564.1.l.a 4 4
2564.1.n \(\chi_{2564}(391, \cdot)\) 2564.1.n.a 8 8
2564.1.o \(\chi_{2564}(255, \cdot)\) 2564.1.o.a 8 8
2564.1.q \(\chi_{2564}(359, \cdot)\) 2564.1.q.a 16 16
2564.1.s \(\chi_{2564}(123, \cdot)\) 2564.1.s.a 16 16
2564.1.u \(\chi_{2564}(159, \cdot)\) None 0 32
2564.1.w \(\chi_{2564}(63, \cdot)\) 2564.1.w.a 32 32
2564.1.y \(\chi_{2564}(21, \cdot)\) None 0 64
2564.1.bb \(\chi_{2564}(11, \cdot)\) 2564.1.bb.a 64 64
2564.1.bd \(\chi_{2564}(7, \cdot)\) None 0 128
2564.1.bf \(\chi_{2564}(17, \cdot)\) None 0 256