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Properties

Label 675.1
Level 675
Weight 1
Dimension 22
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 32400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(32400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(675))\).

Total New Old
Modular forms 870 350 520
Cusp forms 30 22 8
Eisenstein series 840 328 512

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 8

Trace form

\( 22 q - 4 q^{4} - 4 q^{7} + O(q^{10}) \) \( 22 q - 4 q^{4} - 4 q^{7} - 4 q^{10} - 6 q^{16} + 4 q^{19} - 4 q^{22} + 2 q^{25} + 2 q^{28} + 2 q^{31} + 4 q^{34} + 4 q^{37} - 2 q^{40} - 14 q^{46} + 2 q^{49} - 8 q^{55} - 2 q^{58} - 12 q^{61} - 8 q^{64} - 4 q^{67} + 12 q^{70} + 4 q^{76} - 4 q^{79} + 4 q^{82} + 2 q^{85} - 2 q^{88} - 8 q^{91} + 6 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(675))\)

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
675.1.c \(\chi_{675}(26, \cdot)\) 675.1.c.a 1 1
675.1.c.b 1
675.1.c.c 2
675.1.d \(\chi_{675}(674, \cdot)\) 675.1.d.a 2 1
675.1.g \(\chi_{675}(82, \cdot)\) 675.1.g.a 4 2
675.1.g.b 4
675.1.i \(\chi_{675}(224, \cdot)\) None 0 2
675.1.j \(\chi_{675}(251, \cdot)\) None 0 2
675.1.m \(\chi_{675}(134, \cdot)\) None 0 4
675.1.o \(\chi_{675}(161, \cdot)\) 675.1.o.a 8 4
675.1.p \(\chi_{675}(118, \cdot)\) None 0 4
675.1.s \(\chi_{675}(74, \cdot)\) None 0 6
675.1.t \(\chi_{675}(101, \cdot)\) None 0 6
675.1.v \(\chi_{675}(28, \cdot)\) None 0 8
675.1.x \(\chi_{675}(71, \cdot)\) None 0 8
675.1.z \(\chi_{675}(44, \cdot)\) None 0 8
675.1.bb \(\chi_{675}(7, \cdot)\) None 0 12
675.1.be \(\chi_{675}(37, \cdot)\) None 0 16
675.1.bf \(\chi_{675}(11, \cdot)\) None 0 24
675.1.bh \(\chi_{675}(14, \cdot)\) None 0 24
675.1.bj \(\chi_{675}(13, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 1}\)