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Properties

Label 1265.1
Level 1265
Weight 1
Dimension 64
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 126720
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1265 = 5 \cdot 11 \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(126720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1265))\).

Total New Old
Modular forms 1850 1200 650
Cusp forms 90 64 26
Eisenstein series 1760 1136 624

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q + 2 q^{4} + 2 q^{5} - 2 q^{9} + O(q^{10}) \) \( 64 q + 2 q^{4} + 2 q^{5} - 2 q^{9} + 2 q^{11} - 11 q^{15} - 2 q^{16} - 2 q^{20} - 2 q^{25} + 4 q^{31} - 22 q^{33} + 2 q^{36} - 2 q^{44} + 2 q^{45} + 2 q^{49} - 2 q^{55} - 4 q^{59} - 11 q^{60} + 2 q^{64} - 22 q^{69} - 26 q^{71} - 11 q^{75} - 9 q^{80} - 2 q^{81} + 4 q^{89} + 22 q^{97} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1265))\)

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
1265.1.c \(\chi_{1265}(804, \cdot)\) None 0 1
1265.1.d \(\chi_{1265}(461, \cdot)\) None 0 1
1265.1.g \(\chi_{1265}(714, \cdot)\) None 0 1
1265.1.h \(\chi_{1265}(551, \cdot)\) None 0 1
1265.1.j \(\chi_{1265}(252, \cdot)\) 1265.1.j.a 2 2
1265.1.j.b 2
1265.1.k \(\chi_{1265}(507, \cdot)\) None 0 2
1265.1.n \(\chi_{1265}(91, \cdot)\) None 0 4
1265.1.o \(\chi_{1265}(24, \cdot)\) None 0 4
1265.1.r \(\chi_{1265}(116, \cdot)\) None 0 4
1265.1.s \(\chi_{1265}(114, \cdot)\) None 0 4
1265.1.w \(\chi_{1265}(47, \cdot)\) None 0 8
1265.1.x \(\chi_{1265}(68, \cdot)\) None 0 8
1265.1.z \(\chi_{1265}(56, \cdot)\) None 0 10
1265.1.ba \(\chi_{1265}(54, \cdot)\) 1265.1.ba.a 10 10
1265.1.ba.b 10
1265.1.bd \(\chi_{1265}(131, \cdot)\) None 0 10
1265.1.be \(\chi_{1265}(34, \cdot)\) None 0 10
1265.1.bh \(\chi_{1265}(12, \cdot)\) None 0 20
1265.1.bi \(\chi_{1265}(43, \cdot)\) 1265.1.bi.a 20 20
1265.1.bi.b 20
1265.1.bm \(\chi_{1265}(14, \cdot)\) None 0 40
1265.1.bn \(\chi_{1265}(6, \cdot)\) None 0 40
1265.1.bq \(\chi_{1265}(29, \cdot)\) None 0 40
1265.1.br \(\chi_{1265}(86, \cdot)\) None 0 40
1265.1.bt \(\chi_{1265}(7, \cdot)\) None 0 80
1265.1.bu \(\chi_{1265}(3, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1265))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1265)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 2}\)