Properties

Label 75.14
Level 75
Weight 14
Dimension 1777
Nonzero newspaces 6
Sturm bound 5600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(75))\).

Total New Old
Modular forms 2656 1817 839
Cusp forms 2544 1777 767
Eisenstein series 112 40 72

Trace form

\( 1777 q + 190 q^{2} + 3119 q^{3} - 36704 q^{4} + 80394 q^{5} - 1596 q^{6} - 457956 q^{7} + 5622672 q^{8} - 531451 q^{9} + 13131776 q^{10} + 9331852 q^{11} - 72303790 q^{12} - 100724786 q^{13} + 359155680 q^{14}+ \cdots - 7959432246516 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(75))\)

We only show spaces with even 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
75.14.a \(\chi_{75}(1, \cdot)\) 75.14.a.a 1 1
75.14.a.b 1
75.14.a.c 2
75.14.a.d 2
75.14.a.e 2
75.14.a.f 3
75.14.a.g 4
75.14.a.h 4
75.14.a.i 5
75.14.a.j 5
75.14.a.k 6
75.14.a.l 6
75.14.b \(\chi_{75}(49, \cdot)\) 75.14.b.a 2 1
75.14.b.b 2
75.14.b.c 4
75.14.b.d 4
75.14.b.e 4
75.14.b.f 6
75.14.b.g 8
75.14.b.h 10
75.14.e \(\chi_{75}(32, \cdot)\) n/a 152 2
75.14.g \(\chi_{75}(16, \cdot)\) n/a 264 4
75.14.i \(\chi_{75}(4, \cdot)\) n/a 256 4
75.14.l \(\chi_{75}(2, \cdot)\) n/a 1024 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)