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Properties

Label 1975.1
Level 1975
Weight 1
Dimension 53
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 312000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1975 = 5^{2} \cdot 79 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(312000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1975))\).

Total New Old
Modular forms 2257 1632 625
Cusp forms 73 53 20
Eisenstein series 2184 1579 605

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 53 0 0 0

Trace form

\( 53 q + q^{2} + 2 q^{4} + 2 q^{8} + q^{9} + O(q^{10}) \) \( 53 q + q^{2} + 2 q^{4} + 2 q^{8} + q^{9} - 3 q^{11} + q^{13} - 3 q^{16} + q^{18} + q^{19} - 10 q^{20} - 4 q^{21} - 13 q^{22} + q^{23} - q^{26} - 7 q^{31} - 12 q^{32} + 2 q^{38} + 40 q^{40} + 3 q^{44} - 6 q^{46} + q^{49} - 10 q^{50} - 4 q^{51} + 3 q^{52} + 37 q^{62} + 4 q^{64} + q^{67} + 2 q^{72} + q^{73} - 4 q^{76} - 15 q^{79} - q^{81} - 14 q^{83} + 4 q^{84} - 11 q^{88} + q^{89} - 12 q^{92} + q^{97} + q^{98} + q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1975))\)

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
1975.1.c \(\chi_{1975}(1974, \cdot)\) 1975.1.c.a 4 1
1975.1.d \(\chi_{1975}(1026, \cdot)\) 1975.1.d.a 1 1
1975.1.d.b 2
1975.1.d.c 2
1975.1.d.d 4
1975.1.g \(\chi_{1975}(1107, \cdot)\) None 0 2
1975.1.i \(\chi_{1975}(451, \cdot)\) None 0 2
1975.1.j \(\chi_{1975}(24, \cdot)\) None 0 2
1975.1.l \(\chi_{1975}(236, \cdot)\) 1975.1.l.a 20 4
1975.1.m \(\chi_{1975}(394, \cdot)\) 1975.1.m.a 20 4
1975.1.o \(\chi_{1975}(418, \cdot)\) None 0 4
1975.1.s \(\chi_{1975}(238, \cdot)\) None 0 8
1975.1.u \(\chi_{1975}(251, \cdot)\) None 0 12
1975.1.v \(\chi_{1975}(199, \cdot)\) None 0 12
1975.1.y \(\chi_{1975}(214, \cdot)\) None 0 8
1975.1.z \(\chi_{1975}(56, \cdot)\) None 0 8
1975.1.bb \(\chi_{1975}(18, \cdot)\) None 0 24
1975.1.be \(\chi_{1975}(23, \cdot)\) None 0 16
1975.1.bh \(\chi_{1975}(74, \cdot)\) None 0 24
1975.1.bi \(\chi_{1975}(126, \cdot)\) None 0 24
1975.1.bk \(\chi_{1975}(14, \cdot)\) None 0 48
1975.1.bl \(\chi_{1975}(41, \cdot)\) None 0 48
1975.1.bn \(\chi_{1975}(32, \cdot)\) None 0 48
1975.1.bq \(\chi_{1975}(8, \cdot)\) None 0 96
1975.1.br \(\chi_{1975}(6, \cdot)\) None 0 96
1975.1.bs \(\chi_{1975}(29, \cdot)\) None 0 96
1975.1.bu \(\chi_{1975}(2, \cdot)\) None 0 192

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1975))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1975)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(395))\)\(^{\oplus 2}\)