Properties

Label 175.10
Level 175
Weight 10
Dimension 9437
Nonzero newspaces 12
Sturm bound 24000
Trace bound 2

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(24000\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(175))\).

Total New Old
Modular forms 10968 9641 1327
Cusp forms 10632 9437 1195
Eisenstein series 336 204 132

Trace form

\( 9437 q - 91 q^{2} + 727 q^{3} - 3107 q^{4} + 3502 q^{5} - 14270 q^{6} + 13223 q^{7} + 491 q^{8} - 20925 q^{9} - 140848 q^{10} + 425037 q^{11} + 989946 q^{12} - 369660 q^{13} - 1772369 q^{14} - 326016 q^{15}+ \cdots - 1365247596 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.10.a \(\chi_{175}(1, \cdot)\) 175.10.a.a 1 1
175.10.a.b 2
175.10.a.c 2
175.10.a.d 3
175.10.a.e 4
175.10.a.f 5
175.10.a.g 6
175.10.a.h 8
175.10.a.i 8
175.10.a.j 10
175.10.a.k 10
175.10.a.l 13
175.10.a.m 13
175.10.b \(\chi_{175}(99, \cdot)\) 175.10.b.a 2 1
175.10.b.b 4
175.10.b.c 4
175.10.b.d 6
175.10.b.e 8
175.10.b.f 10
175.10.b.g 12
175.10.b.h 16
175.10.b.i 20
175.10.e \(\chi_{175}(51, \cdot)\) n/a 222 2
175.10.f \(\chi_{175}(118, \cdot)\) n/a 212 2
175.10.h \(\chi_{175}(36, \cdot)\) n/a 544 4
175.10.k \(\chi_{175}(74, \cdot)\) n/a 212 2
175.10.n \(\chi_{175}(29, \cdot)\) n/a 536 4
175.10.o \(\chi_{175}(68, \cdot)\) n/a 424 4
175.10.q \(\chi_{175}(11, \cdot)\) n/a 1424 8
175.10.s \(\chi_{175}(13, \cdot)\) n/a 1424 8
175.10.t \(\chi_{175}(4, \cdot)\) n/a 1424 8
175.10.x \(\chi_{175}(3, \cdot)\) n/a 2848 16

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)