Properties

Label 475.1
Level 475
Weight 1
Dimension 11
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 18000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(18000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(475))\).

Total New Old
Modular forms 521 360 161
Cusp forms 17 11 6
Eisenstein series 504 349 155

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 11 0 0 0

Trace form

\( 11 q - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} - q^{9} + O(q^{10}) \) \( 11 q - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{7} - q^{9} - 2 q^{11} - 3 q^{16} + 8 q^{17} - q^{19} - 2 q^{23} - 2 q^{25} + 4 q^{26} - 2 q^{28} + 8 q^{35} + q^{36} + 4 q^{39} - 2 q^{43} - 6 q^{44} - 2 q^{47} - 7 q^{49} - 2 q^{61} - 2 q^{63} + 3 q^{64} - 2 q^{68} - 2 q^{73} + 4 q^{74} - 3 q^{76} - 4 q^{77} - 2 q^{80} - 3 q^{81} + 8 q^{83} - 2 q^{85} - 2 q^{92} - 2 q^{95} + 4 q^{96} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(475))\)

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
475.1.c \(\chi_{475}(151, \cdot)\) 475.1.c.a 1 1
475.1.c.b 2
475.1.d \(\chi_{475}(474, \cdot)\) None 0 1
475.1.f \(\chi_{475}(343, \cdot)\) None 0 2
475.1.i \(\chi_{475}(274, \cdot)\) None 0 2
475.1.k \(\chi_{475}(126, \cdot)\) None 0 2
475.1.m \(\chi_{475}(94, \cdot)\) 475.1.m.a 4 4
475.1.o \(\chi_{475}(56, \cdot)\) 475.1.o.a 4 4
475.1.q \(\chi_{475}(7, \cdot)\) None 0 4
475.1.s \(\chi_{475}(51, \cdot)\) None 0 6
475.1.t \(\chi_{475}(124, \cdot)\) None 0 6
475.1.w \(\chi_{475}(58, \cdot)\) None 0 8
475.1.y \(\chi_{475}(31, \cdot)\) None 0 8
475.1.z \(\chi_{475}(69, \cdot)\) None 0 8
475.1.ba \(\chi_{475}(43, \cdot)\) None 0 12
475.1.bd \(\chi_{475}(83, \cdot)\) None 0 16
475.1.bf \(\chi_{475}(21, \cdot)\) None 0 24
475.1.bh \(\chi_{475}(14, \cdot)\) None 0 24
475.1.bj \(\chi_{475}(17, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)