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Properties

Label 465.1
Level 465
Weight 1
Dimension 28
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 15360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(15360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(465))\).

Total New Old
Modular forms 526 204 322
Cusp forms 46 28 18
Eisenstein series 480 176 304

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q - 6 q^{4} - 4 q^{6} - 2 q^{9} - 4 q^{10} - 2 q^{15} - 10 q^{16} - 4 q^{19} + 22 q^{24} - 2 q^{25} - 2 q^{31} - 8 q^{34} - 6 q^{36} + 22 q^{40} - 8 q^{46} - 2 q^{49} - 4 q^{51} - 4 q^{54} - 6 q^{60}+ \cdots - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(465))\)

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
465.1.b \(\chi_{465}(154, \cdot)\) None 0 1
465.1.d \(\chi_{465}(311, \cdot)\) None 0 1
465.1.f \(\chi_{465}(404, \cdot)\) None 0 1
465.1.h \(\chi_{465}(61, \cdot)\) None 0 1
465.1.l \(\chi_{465}(187, \cdot)\) None 0 2
465.1.m \(\chi_{465}(92, \cdot)\) None 0 2
465.1.p \(\chi_{465}(56, \cdot)\) None 0 2
465.1.r \(\chi_{465}(274, \cdot)\) None 0 2
465.1.s \(\chi_{465}(181, \cdot)\) None 0 2
465.1.u \(\chi_{465}(149, \cdot)\) 465.1.u.a 2 2
465.1.u.b 2
465.1.v \(\chi_{465}(46, \cdot)\) None 0 4
465.1.x \(\chi_{465}(194, \cdot)\) 465.1.x.a 4 4
465.1.x.b 4
465.1.z \(\chi_{465}(101, \cdot)\) None 0 4
465.1.bb \(\chi_{465}(139, \cdot)\) None 0 4
465.1.bc \(\chi_{465}(68, \cdot)\) None 0 4
465.1.bd \(\chi_{465}(67, \cdot)\) None 0 4
465.1.bh \(\chi_{465}(23, \cdot)\) None 0 8
465.1.bi \(\chi_{465}(97, \cdot)\) None 0 8
465.1.bl \(\chi_{465}(14, \cdot)\) 465.1.bl.a 8 8
465.1.bl.b 8
465.1.bn \(\chi_{465}(106, \cdot)\) None 0 8
465.1.bo \(\chi_{465}(34, \cdot)\) None 0 8
465.1.bq \(\chi_{465}(41, \cdot)\) None 0 8
465.1.bu \(\chi_{465}(7, \cdot)\) None 0 16
465.1.bv \(\chi_{465}(17, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(465))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(465)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)