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

\( 7902 q - 103 q^{2} - 105 q^{3} - 111 q^{4} - 134 q^{5} - 177 q^{6} - 113 q^{7} - 127 q^{8} - 123 q^{9} - 154 q^{10} - 177 q^{11} - 165 q^{12} - 137 q^{13} - 163 q^{14} - 164 q^{15} - 219 q^{16} - 122 q^{17}+ \cdots + 292 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)