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Properties

Label 915.1
Level 915
Weight 1
Dimension 58
Nonzero newspaces 7
Newform subspaces 14
Sturm bound 59520
Trace bound 4

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Defining parameters

Level: \( N \) = \( 915 = 3 \cdot 5 \cdot 61 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 14 \)
Sturm bound: \(59520\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(915))\).

Total New Old
Modular forms 1040 414 626
Cusp forms 80 58 22
Eisenstein series 960 356 604

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 58 0 0 0

Trace form

\( 58 q - 6 q^{4} - 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 58 q - 6 q^{4} - 4 q^{6} - 2 q^{9} - 4 q^{10} - 2 q^{15} - 10 q^{16} - 4 q^{19} - 8 q^{24} - 2 q^{25} - 4 q^{31} - 8 q^{34} - 6 q^{36} - 8 q^{40} - 8 q^{46} - 2 q^{49} - 4 q^{51} - 4 q^{54} + 54 q^{60} - 2 q^{61} + 46 q^{64} - 4 q^{69} - 12 q^{76} - 4 q^{79} - 2 q^{81} - 4 q^{85} - 4 q^{90} - 8 q^{94} - 12 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(915))\)

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
915.1.d \(\chi_{915}(611, \cdot)\) None 0 1
915.1.e \(\chi_{915}(914, \cdot)\) 915.1.e.a 1 1
915.1.e.b 1
915.1.f \(\chi_{915}(794, \cdot)\) None 0 1
915.1.g \(\chi_{915}(731, \cdot)\) None 0 1
915.1.k \(\chi_{915}(743, \cdot)\) None 0 2
915.1.l \(\chi_{915}(487, \cdot)\) None 0 2
915.1.n \(\chi_{915}(499, \cdot)\) None 0 2
915.1.p \(\chi_{915}(316, \cdot)\) None 0 2
915.1.r \(\chi_{915}(367, \cdot)\) None 0 2
915.1.t \(\chi_{915}(233, \cdot)\) None 0 2
915.1.x \(\chi_{915}(74, \cdot)\) 915.1.x.a 2 2
915.1.x.b 2
915.1.y \(\chi_{915}(536, \cdot)\) None 0 2
915.1.z \(\chi_{915}(596, \cdot)\) None 0 2
915.1.ba \(\chi_{915}(14, \cdot)\) 915.1.ba.a 2 2
915.1.ba.b 2
915.1.be \(\chi_{915}(119, \cdot)\) 915.1.be.a 4 4
915.1.be.b 4
915.1.bf \(\chi_{915}(41, \cdot)\) None 0 4
915.1.bg \(\chi_{915}(131, \cdot)\) None 0 4
915.1.bh \(\chi_{915}(149, \cdot)\) 915.1.bh.a 4 4
915.1.bh.b 4
915.1.bl \(\chi_{915}(212, \cdot)\) None 0 4
915.1.bn \(\chi_{915}(292, \cdot)\) None 0 4
915.1.bp \(\chi_{915}(151, \cdot)\) None 0 4
915.1.br \(\chi_{915}(154, \cdot)\) None 0 4
915.1.bt \(\chi_{915}(13, \cdot)\) None 0 4
915.1.bu \(\chi_{915}(32, \cdot)\) None 0 4
915.1.by \(\chi_{915}(23, \cdot)\) None 0 8
915.1.bz \(\chi_{915}(52, \cdot)\) None 0 8
915.1.cb \(\chi_{915}(94, \cdot)\) None 0 8
915.1.cd \(\chi_{915}(211, \cdot)\) None 0 8
915.1.cf \(\chi_{915}(58, \cdot)\) None 0 8
915.1.ch \(\chi_{915}(8, \cdot)\) None 0 8
915.1.cl \(\chi_{915}(56, \cdot)\) None 0 8
915.1.cm \(\chi_{915}(344, \cdot)\) 915.1.cm.a 8 8
915.1.cm.b 8
915.1.cn \(\chi_{915}(134, \cdot)\) 915.1.cn.a 8 8
915.1.cn.b 8
915.1.co \(\chi_{915}(161, \cdot)\) None 0 8
915.1.cr \(\chi_{915}(2, \cdot)\) None 0 16
915.1.ct \(\chi_{915}(97, \cdot)\) None 0 16
915.1.cv \(\chi_{915}(31, \cdot)\) None 0 16
915.1.cx \(\chi_{915}(79, \cdot)\) None 0 16
915.1.cz \(\chi_{915}(22, \cdot)\) None 0 16
915.1.da \(\chi_{915}(17, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(915))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(915)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(305))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(915))\)\(^{\oplus 1}\)