Properties

Label 175.8
Level 175
Weight 8
Dimension 7317
Nonzero newspaces 12
Sturm bound 19200
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(19200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(175))\).

Total New Old
Modular forms 8568 7521 1047
Cusp forms 8232 7317 915
Eisenstein series 336 204 132

Trace form

\( 7317 q + 5 q^{2} - 104 q^{3} + 477 q^{4} + 22 q^{5} - 2894 q^{6} - 3185 q^{7} + 7235 q^{8} + 31155 q^{9} + O(q^{10}) \) \( 7317 q + 5 q^{2} - 104 q^{3} + 477 q^{4} + 22 q^{5} - 2894 q^{6} - 3185 q^{7} + 7235 q^{8} + 31155 q^{9} + 3072 q^{10} - 34536 q^{11} - 86142 q^{12} + 24622 q^{13} + 125599 q^{14} + 17724 q^{15} - 76103 q^{16} - 357890 q^{17} - 218813 q^{18} + 294216 q^{19} + 619292 q^{20} + 351294 q^{21} + 130440 q^{22} - 1038564 q^{23} - 2814962 q^{24} - 900426 q^{25} - 769764 q^{26} + 1466884 q^{27} + 3199627 q^{28} + 2074518 q^{29} + 3696964 q^{30} + 1036676 q^{31} - 3031545 q^{32} - 7414068 q^{33} - 8426554 q^{34} - 1145792 q^{35} - 2039571 q^{36} + 3653924 q^{37} + 5524868 q^{38} + 3959832 q^{39} - 269896 q^{40} + 2106526 q^{41} + 3446864 q^{42} + 3285080 q^{43} + 7016368 q^{44} + 1775978 q^{45} - 11932594 q^{46} - 3422012 q^{47} - 16382862 q^{48} - 1248443 q^{49} - 17917396 q^{50} - 3422052 q^{51} - 3124832 q^{52} - 6112444 q^{53} + 30418166 q^{54} + 19588916 q^{55} - 7964671 q^{56} + 9456956 q^{57} - 14725610 q^{58} + 10320180 q^{59} - 25790428 q^{60} + 14576178 q^{61} - 10679412 q^{62} + 19733437 q^{63} + 34440025 q^{64} + 27601994 q^{65} + 16319174 q^{66} + 5755624 q^{67} - 29944678 q^{68} - 36712292 q^{69} - 50542578 q^{70} - 12574396 q^{71} - 113817453 q^{72} - 25233798 q^{73} - 19506708 q^{74} - 23851892 q^{75} + 84762674 q^{76} + 57023646 q^{77} + 146803448 q^{78} + 71674892 q^{79} + 102557648 q^{80} + 16066851 q^{81} + 9984486 q^{82} - 18933360 q^{83} - 149583800 q^{84} - 130549678 q^{85} + 63986208 q^{86} - 56513236 q^{87} - 118030560 q^{88} - 86697888 q^{89} + 31952580 q^{90} - 35100608 q^{91} + 194891868 q^{92} + 303939736 q^{93} + 245610986 q^{94} + 59125468 q^{95} + 283712162 q^{96} - 55688594 q^{97} + 4846583 q^{98} - 218218500 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.8.a \(\chi_{175}(1, \cdot)\) 175.8.a.a 1 1
175.8.a.b 2
175.8.a.c 2
175.8.a.d 3
175.8.a.e 4
175.8.a.f 5
175.8.a.g 6
175.8.a.h 6
175.8.a.i 8
175.8.a.j 8
175.8.a.k 11
175.8.a.l 11
175.8.b \(\chi_{175}(99, \cdot)\) 175.8.b.a 2 1
175.8.b.b 4
175.8.b.c 4
175.8.b.d 6
175.8.b.e 8
175.8.b.f 10
175.8.b.g 12
175.8.b.h 16
175.8.e \(\chi_{175}(51, \cdot)\) n/a 172 2
175.8.f \(\chi_{175}(118, \cdot)\) n/a 164 2
175.8.h \(\chi_{175}(36, \cdot)\) n/a 416 4
175.8.k \(\chi_{175}(74, \cdot)\) n/a 164 2
175.8.n \(\chi_{175}(29, \cdot)\) n/a 424 4
175.8.o \(\chi_{175}(68, \cdot)\) n/a 328 4
175.8.q \(\chi_{175}(11, \cdot)\) n/a 1104 8
175.8.s \(\chi_{175}(13, \cdot)\) n/a 1104 8
175.8.t \(\chi_{175}(4, \cdot)\) n/a 1104 8
175.8.x \(\chi_{175}(3, \cdot)\) n/a 2208 16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 1}\)