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Properties

Label 475.2
Level 475
Weight 2
Dimension 7902
Nonzero newspaces 18
Newform subspaces 65
Sturm bound 36000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 65 \)
Sturm bound: \(36000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(475))\).

Total New Old
Modular forms 9504 8598 906
Cusp forms 8497 7902 595
Eisenstein series 1007 696 311

Trace form

\( 7902 q - 103 q^{2} - 105 q^{3} - 111 q^{4} - 134 q^{5} - 177 q^{6} - 113 q^{7} - 127 q^{8} - 123 q^{9} + O(q^{10}) \) \( 7902 q - 103 q^{2} - 105 q^{3} - 111 q^{4} - 134 q^{5} - 177 q^{6} - 113 q^{7} - 127 q^{8} - 123 q^{9} - 154 q^{10} - 177 q^{11} - 165 q^{12} - 137 q^{13} - 163 q^{14} - 164 q^{15} - 219 q^{16} - 122 q^{17} - 161 q^{18} - 128 q^{19} - 268 q^{20} - 198 q^{21} - 116 q^{22} - 114 q^{23} - 113 q^{24} - 114 q^{25} - 375 q^{26} - 138 q^{27} - 128 q^{28} - 135 q^{29} - 164 q^{30} - 195 q^{31} - 198 q^{32} - 207 q^{33} - 200 q^{34} - 184 q^{35} - 331 q^{36} - 190 q^{37} - 200 q^{38} - 300 q^{39} - 174 q^{40} - 215 q^{41} - 179 q^{42} - 144 q^{43} - 197 q^{44} - 94 q^{45} - 258 q^{46} - 158 q^{47} - 171 q^{48} - 140 q^{49} - 94 q^{50} - 391 q^{51} - 139 q^{52} - 151 q^{53} - 158 q^{54} - 164 q^{55} - 326 q^{56} - 152 q^{57} - 290 q^{58} - 162 q^{59} - 124 q^{60} - 263 q^{61} - 168 q^{62} - 209 q^{63} - 269 q^{64} - 154 q^{65} - 369 q^{66} - 246 q^{67} - 235 q^{68} - 248 q^{69} - 204 q^{70} - 280 q^{71} - 57 q^{72} - 249 q^{73} - 195 q^{74} - 164 q^{75} - 459 q^{76} - 273 q^{77} - 29 q^{78} - 135 q^{79} + 62 q^{80} - 72 q^{81} + 8 q^{82} + 108 q^{83} + 503 q^{84} + 70 q^{85} + 12 q^{86} + 355 q^{87} + 501 q^{88} + 108 q^{89} + 266 q^{90} + 27 q^{91} + 306 q^{92} + 381 q^{93} + 466 q^{94} - 46 q^{95} + 530 q^{96} + 140 q^{97} + 286 q^{98} + 292 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
475.2.a \(\chi_{475}(1, \cdot)\) 475.2.a.a 1 1
475.2.a.b 1
475.2.a.c 1
475.2.a.d 3
475.2.a.e 3
475.2.a.f 3
475.2.a.g 3
475.2.a.h 3
475.2.a.i 4
475.2.a.j 6
475.2.b \(\chi_{475}(324, \cdot)\) 475.2.b.a 2 1
475.2.b.b 6
475.2.b.c 6
475.2.b.d 6
475.2.b.e 8
475.2.e \(\chi_{475}(26, \cdot)\) 475.2.e.a 2 2
475.2.e.b 2
475.2.e.c 2
475.2.e.d 6
475.2.e.e 8
475.2.e.f 12
475.2.e.g 12
475.2.e.h 12
475.2.g \(\chi_{475}(18, \cdot)\) 475.2.g.a 4 2
475.2.g.b 12
475.2.g.c 16
475.2.g.d 24
475.2.h \(\chi_{475}(96, \cdot)\) 475.2.h.a 84 4
475.2.h.b 100
475.2.j \(\chi_{475}(49, \cdot)\) 475.2.j.a 4 2
475.2.j.b 12
475.2.j.c 16
475.2.j.d 24
475.2.l \(\chi_{475}(101, \cdot)\) 475.2.l.a 6 6
475.2.l.b 18
475.2.l.c 18
475.2.l.d 42
475.2.l.e 42
475.2.l.f 48
475.2.n \(\chi_{475}(39, \cdot)\) 475.2.n.a 80 4
475.2.n.b 96
475.2.p \(\chi_{475}(107, \cdot)\) 475.2.p.a 4 4
475.2.p.b 4
475.2.p.c 4
475.2.p.d 4
475.2.p.e 16
475.2.p.f 16
475.2.p.g 16
475.2.p.h 24
475.2.p.i 24
475.2.r \(\chi_{475}(11, \cdot)\) 475.2.r.a 384 8
475.2.u \(\chi_{475}(24, \cdot)\) 475.2.u.a 12 6
475.2.u.b 36
475.2.u.c 36
475.2.u.d 84
475.2.v \(\chi_{475}(37, \cdot)\) 475.2.v.a 16 8
475.2.v.b 368
475.2.x \(\chi_{475}(64, \cdot)\) 475.2.x.a 384 8
475.2.bb \(\chi_{475}(32, \cdot)\) 475.2.bb.a 72 12
475.2.bb.b 96
475.2.bb.c 168
475.2.bc \(\chi_{475}(6, \cdot)\) 475.2.bc.a 1152 24
475.2.be \(\chi_{475}(8, \cdot)\) 475.2.be.a 768 16
475.2.bg \(\chi_{475}(4, \cdot)\) 475.2.bg.a 1152 24
475.2.bi \(\chi_{475}(2, \cdot)\) 475.2.bi.a 2304 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)