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Properties

Label 335.1
Level 335
Weight 1
Dimension 8
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 8976
Trace bound 0

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Defining parameters

Level: \( N \) = \( 335 = 5 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(8976\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(335))\).

Total New Old
Modular forms 272 202 70
Cusp forms 8 8 0
Eisenstein series 264 194 70

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 6 q^{4} - 4 q^{6} + 6 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{4} - 4 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{14} - 2 q^{15} + 4 q^{16} - 2 q^{19} - 4 q^{21} - 8 q^{24} + 8 q^{25} - 4 q^{26} - 2 q^{29} - 2 q^{35} - 4 q^{39} - 4 q^{40} + 6 q^{49} - 8 q^{54} - 8 q^{56} - 2 q^{59} - 6 q^{60} + 2 q^{64} - 2 q^{65} - 2 q^{71} - 6 q^{76} + 4 q^{81} + 6 q^{84} + 14 q^{86} - 2 q^{89} + 12 q^{90} - 4 q^{91} + 6 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(335))\)

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
335.1.b \(\chi_{335}(66, \cdot)\) None 0 1
335.1.d \(\chi_{335}(334, \cdot)\) 335.1.d.a 1 1
335.1.d.b 1
335.1.d.c 3
335.1.d.d 3
335.1.g \(\chi_{335}(68, \cdot)\) None 0 2
335.1.h \(\chi_{335}(164, \cdot)\) None 0 2
335.1.j \(\chi_{335}(231, \cdot)\) None 0 2
335.1.l \(\chi_{335}(37, \cdot)\) None 0 4
335.1.n \(\chi_{335}(94, \cdot)\) None 0 10
335.1.p \(\chi_{335}(161, \cdot)\) None 0 10
335.1.r \(\chi_{335}(22, \cdot)\) None 0 20
335.1.t \(\chi_{335}(11, \cdot)\) None 0 20
335.1.v \(\chi_{335}(34, \cdot)\) None 0 20
335.1.x \(\chi_{335}(17, \cdot)\) None 0 40