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Properties

Label 2025.1
Level 2025
Weight 1
Dimension 48
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 291600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(291600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2025))\).

Total New Old
Modular forms 3138 1196 1942
Cusp forms 114 48 66
Eisenstein series 3024 1148 1876

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 16

Trace form

\( 48 q + 4 q^{4} + 4 q^{7} + O(q^{10}) \) \( 48 q + 4 q^{4} + 4 q^{7} - 8 q^{10} + 8 q^{16} + 8 q^{19} + 4 q^{22} - 2 q^{25} + 4 q^{28} + 2 q^{31} - 4 q^{34} + 8 q^{37} + 2 q^{40} - 28 q^{46} - 2 q^{49} - 16 q^{55} + 2 q^{58} + 8 q^{61} - 16 q^{64} + 4 q^{67} - 12 q^{70} - 8 q^{76} + 4 q^{79} + 8 q^{82} - 2 q^{85} + 2 q^{88} - 16 q^{91} - 6 q^{94} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2025))\)

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
2025.1.c \(\chi_{2025}(1376, \cdot)\) None 0 1
2025.1.d \(\chi_{2025}(2024, \cdot)\) None 0 1
2025.1.g \(\chi_{2025}(82, \cdot)\) None 0 2
2025.1.i \(\chi_{2025}(674, \cdot)\) 2025.1.i.a 4 2
2025.1.j \(\chi_{2025}(26, \cdot)\) 2025.1.j.a 2 2
2025.1.j.b 2
2025.1.j.c 4
2025.1.m \(\chi_{2025}(404, \cdot)\) None 0 4
2025.1.o \(\chi_{2025}(161, \cdot)\) None 0 4
2025.1.p \(\chi_{2025}(757, \cdot)\) 2025.1.p.a 4 4
2025.1.p.b 8
2025.1.p.c 8
2025.1.s \(\chi_{2025}(224, \cdot)\) None 0 6
2025.1.t \(\chi_{2025}(251, \cdot)\) None 0 6
2025.1.v \(\chi_{2025}(163, \cdot)\) None 0 8
2025.1.y \(\chi_{2025}(296, \cdot)\) 2025.1.y.a 16 8
2025.1.ba \(\chi_{2025}(134, \cdot)\) None 0 8
2025.1.bc \(\chi_{2025}(118, \cdot)\) None 0 12
2025.1.bf \(\chi_{2025}(101, \cdot)\) None 0 18
2025.1.bg \(\chi_{2025}(74, \cdot)\) None 0 18
2025.1.bi \(\chi_{2025}(28, \cdot)\) None 0 16
2025.1.bj \(\chi_{2025}(71, \cdot)\) None 0 24
2025.1.bl \(\chi_{2025}(44, \cdot)\) None 0 24
2025.1.bm \(\chi_{2025}(7, \cdot)\) None 0 36
2025.1.bq \(\chi_{2025}(37, \cdot)\) None 0 48
2025.1.bs \(\chi_{2025}(14, \cdot)\) None 0 72
2025.1.bt \(\chi_{2025}(11, \cdot)\) None 0 72
2025.1.bu \(\chi_{2025}(13, \cdot)\) None 0 144

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2025))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2025)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)