Properties

Label 429.1
Level 429
Weight 1
Dimension 16
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 13440
Trace bound 0

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Defining parameters

Level: \( N \) = \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(13440\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(429))\).

Total New Old
Modular forms 506 216 290
Cusp forms 26 16 10
Eisenstein series 480 200 280

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16q - 4q^{4} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{4} - 4q^{9} - 8q^{10} - 8q^{12} + 8q^{16} - 4q^{22} - 4q^{25} + 12q^{30} - 4q^{36} - 4q^{39} - 16q^{40} - 8q^{43} + 12q^{48} - 4q^{49} + 12q^{52} - 4q^{55} + 8q^{64} - 4q^{66} + 12q^{75} - 4q^{81} + 12q^{82} + 12q^{88} + 12q^{90} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(429))\)

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
429.1.c \(\chi_{429}(287, \cdot)\) None 0 1
429.1.d \(\chi_{429}(274, \cdot)\) None 0 1
429.1.g \(\chi_{429}(142, \cdot)\) None 0 1
429.1.h \(\chi_{429}(155, \cdot)\) None 0 1
429.1.k \(\chi_{429}(34, \cdot)\) None 0 2
429.1.l \(\chi_{429}(164, \cdot)\) None 0 2
429.1.o \(\chi_{429}(10, \cdot)\) None 0 2
429.1.q \(\chi_{429}(23, \cdot)\) None 0 2
429.1.r \(\chi_{429}(386, \cdot)\) None 0 2
429.1.u \(\chi_{429}(373, \cdot)\) None 0 2
429.1.v \(\chi_{429}(38, \cdot)\) 429.1.v.a 4 4
429.1.v.b 4
429.1.v.c 8
429.1.w \(\chi_{429}(259, \cdot)\) None 0 4
429.1.z \(\chi_{429}(40, \cdot)\) None 0 4
429.1.ba \(\chi_{429}(14, \cdot)\) None 0 4
429.1.bc \(\chi_{429}(32, \cdot)\) None 0 4
429.1.bf \(\chi_{429}(67, \cdot)\) None 0 4
429.1.bh \(\chi_{429}(31, \cdot)\) None 0 8
429.1.bk \(\chi_{429}(8, \cdot)\) None 0 8
429.1.bl \(\chi_{429}(61, \cdot)\) None 0 8
429.1.bo \(\chi_{429}(113, \cdot)\) None 0 8
429.1.bp \(\chi_{429}(179, \cdot)\) None 0 8
429.1.br \(\chi_{429}(127, \cdot)\) None 0 8
429.1.bt \(\chi_{429}(2, \cdot)\) None 0 16
429.1.bu \(\chi_{429}(37, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(429))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(429)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)