Properties

Label 405.1
Level 405
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 11664
Trace bound 0

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Defining parameters

Level: \( N \) = \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(11664\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(405))\).

Total New Old
Modular forms 440 172 268
Cusp forms 8 4 4
Eisenstein series 432 168 264

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{10} + 2 q^{16} - 4 q^{19} - 2 q^{25} + 2 q^{31} - 2 q^{34} - 2 q^{40} + 4 q^{46} - 2 q^{49} + 2 q^{61} + 4 q^{64} + 2 q^{79} + 2 q^{85} + 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
405.1.c \(\chi_{405}(161, \cdot)\) None 0 1
405.1.d \(\chi_{405}(404, \cdot)\) None 0 1
405.1.g \(\chi_{405}(82, \cdot)\) None 0 2
405.1.h \(\chi_{405}(134, \cdot)\) 405.1.h.a 2 2
405.1.h.b 2
405.1.i \(\chi_{405}(26, \cdot)\) None 0 2
405.1.l \(\chi_{405}(28, \cdot)\) None 0 4
405.1.n \(\chi_{405}(44, \cdot)\) None 0 6
405.1.o \(\chi_{405}(71, \cdot)\) None 0 6
405.1.s \(\chi_{405}(37, \cdot)\) None 0 12
405.1.u \(\chi_{405}(11, \cdot)\) None 0 18
405.1.v \(\chi_{405}(14, \cdot)\) None 0 18
405.1.w \(\chi_{405}(7, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(405)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)