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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

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

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

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