Properties

Label 175.3
Level 175
Weight 3
Dimension 2017
Nonzero newspaces 12
Newform subspaces 34
Sturm bound 7200
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 34 \)
Sturm bound: \(7200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(175))\).

Total New Old
Modular forms 2568 2223 345
Cusp forms 2232 2017 215
Eisenstein series 336 206 130

Trace form

\( 2017 q - 19 q^{2} - 16 q^{3} - 11 q^{4} - 28 q^{5} - 24 q^{6} - 33 q^{7} - 55 q^{8} - 7 q^{9} + O(q^{10}) \) \( 2017 q - 19 q^{2} - 16 q^{3} - 11 q^{4} - 28 q^{5} - 24 q^{6} - 33 q^{7} - 55 q^{8} - 7 q^{9} - 28 q^{10} - 30 q^{11} - 16 q^{12} - 16 q^{13} - 5 q^{14} - 76 q^{15} - 163 q^{16} - 156 q^{17} - 343 q^{18} - 216 q^{19} - 308 q^{20} - 102 q^{21} - 194 q^{22} - 38 q^{23} - 420 q^{24} - 76 q^{25} - 368 q^{26} - 340 q^{27} - 397 q^{28} - 146 q^{29} + 164 q^{30} + 112 q^{31} + 301 q^{32} + 224 q^{33} + 460 q^{34} + 108 q^{35} + 377 q^{36} + 42 q^{37} - 292 q^{38} - 216 q^{39} - 496 q^{40} - 8 q^{41} + 426 q^{42} - 42 q^{43} + 214 q^{44} - 272 q^{45} + 138 q^{46} + 136 q^{47} + 508 q^{48} + 13 q^{49} + 104 q^{50} + 176 q^{51} + 220 q^{52} + 338 q^{53} + 420 q^{54} + 116 q^{55} - 977 q^{56} + 76 q^{57} - 706 q^{58} - 476 q^{59} - 28 q^{60} - 1216 q^{61} - 1668 q^{62} - 1231 q^{63} - 2283 q^{64} - 1056 q^{65} - 1272 q^{66} - 1078 q^{67} - 1816 q^{68} - 740 q^{69} - 178 q^{70} - 18 q^{71} + 393 q^{72} + 672 q^{73} + 1398 q^{74} + 708 q^{75} + 2016 q^{76} + 1408 q^{77} + 3520 q^{78} + 2210 q^{79} + 2648 q^{80} + 1697 q^{81} + 3024 q^{82} + 1308 q^{83} + 1990 q^{84} - 528 q^{85} + 450 q^{86} - 996 q^{87} - 1166 q^{88} - 1816 q^{89} - 1720 q^{90} - 1590 q^{91} - 3378 q^{92} - 2924 q^{93} - 3536 q^{94} - 1532 q^{95} - 3312 q^{96} - 1584 q^{97} - 2081 q^{98} - 1086 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(175))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
175.3.c \(\chi_{175}(174, \cdot)\) 175.3.c.a 2 1
175.3.c.b 4
175.3.c.c 4
175.3.c.d 4
175.3.c.e 8
175.3.d \(\chi_{175}(76, \cdot)\) 175.3.d.a 1 1
175.3.d.b 2
175.3.d.c 2
175.3.d.d 2
175.3.d.e 2
175.3.d.f 2
175.3.d.g 2
175.3.d.h 2
175.3.d.i 4
175.3.d.j 4
175.3.g \(\chi_{175}(43, \cdot)\) 175.3.g.a 8 2
175.3.g.b 12
175.3.g.c 16
175.3.i \(\chi_{175}(26, \cdot)\) 175.3.i.a 10 2
175.3.i.b 10
175.3.i.c 12
175.3.i.d 12
175.3.j \(\chi_{175}(24, \cdot)\) 175.3.j.a 20 2
175.3.j.b 24
175.3.l \(\chi_{175}(6, \cdot)\) 175.3.l.a 152 4
175.3.m \(\chi_{175}(34, \cdot)\) 175.3.m.a 152 4
175.3.p \(\chi_{175}(18, \cdot)\) 175.3.p.a 8 4
175.3.p.b 16
175.3.p.c 24
175.3.p.d 40
175.3.r \(\chi_{175}(8, \cdot)\) 175.3.r.a 240 8
175.3.u \(\chi_{175}(19, \cdot)\) 175.3.u.a 304 8
175.3.v \(\chi_{175}(31, \cdot)\) 175.3.v.a 304 8
175.3.w \(\chi_{175}(2, \cdot)\) 175.3.w.a 608 16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)