Properties

Label 75.3
Level 75
Weight 3
Dimension 256
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 1200
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(1200\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(75))\).

Total New Old
Modular forms 456 298 158
Cusp forms 344 256 88
Eisenstein series 112 42 70

Trace form

\( 256 q + 8 q^{2} - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 24 q^{8} - 42 q^{9} - 44 q^{10} - 32 q^{11} - 66 q^{12} - 20 q^{13} + 6 q^{15} - 68 q^{16} - 60 q^{17} + 34 q^{18} - 124 q^{19} - 244 q^{20}+ \cdots - 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.3.c \(\chi_{75}(26, \cdot)\) 75.3.c.a 1 1
75.3.c.b 1
75.3.c.c 2
75.3.c.d 2
75.3.c.e 2
75.3.c.f 2
75.3.d \(\chi_{75}(74, \cdot)\) 75.3.d.a 2 1
75.3.d.b 4
75.3.d.c 4
75.3.f \(\chi_{75}(7, \cdot)\) 75.3.f.a 4 2
75.3.f.b 4
75.3.f.c 4
75.3.h \(\chi_{75}(14, \cdot)\) 75.3.h.a 72 4
75.3.j \(\chi_{75}(11, \cdot)\) 75.3.j.a 72 4
75.3.k \(\chi_{75}(13, \cdot)\) 75.3.k.a 80 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)