Properties

Label 507.2
Level 507
Weight 2
Dimension 6811
Nonzero newspaces 12
Newform subspaces 69
Sturm bound 37856
Trace bound 1

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Defining parameters

Level: \( N \) = \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 69 \)
Sturm bound: \(37856\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(507))\).

Total New Old
Modular forms 9920 7219 2701
Cusp forms 9009 6811 2198
Eisenstein series 911 408 503

Trace form

\( 6811q + 3q^{2} - 65q^{3} - 125q^{4} + 6q^{5} - 63q^{6} - 132q^{7} - 21q^{8} - 69q^{9} + O(q^{10}) \) \( 6811q + 3q^{2} - 65q^{3} - 125q^{4} + 6q^{5} - 63q^{6} - 132q^{7} - 21q^{8} - 69q^{9} - 174q^{10} - 12q^{11} - 111q^{12} - 168q^{13} - 24q^{14} - 84q^{15} - 181q^{16} - 18q^{17} - 111q^{18} - 192q^{19} - 90q^{20} - 110q^{21} - 216q^{22} - 24q^{23} - 123q^{24} - 185q^{25} - 60q^{26} - 197q^{27} - 244q^{28} - 30q^{29} - 96q^{30} - 148q^{31} - 57q^{32} - 66q^{33} - 174q^{34} + q^{36} - 106q^{37} + 60q^{38} - 56q^{39} - 258q^{40} - 42q^{41} - 78q^{42} - 216q^{43} - 36q^{44} - 36q^{45} - 300q^{46} - 48q^{47} - 107q^{48} - 251q^{49} - 135q^{50} - 156q^{51} - 294q^{52} - 138q^{53} - 159q^{54} - 324q^{55} - 240q^{56} - 194q^{57} - 342q^{58} - 108q^{59} - 228q^{60} - 298q^{61} - 168q^{62} - 110q^{63} - 353q^{64} - 90q^{65} - 114q^{66} - 192q^{67} - 54q^{68} - 54q^{69} - 252q^{70} + 24q^{71} - 39q^{72} - 138q^{73} - 42q^{74} - 39q^{75} - 216q^{76} - 48q^{77} - 18q^{78} - 316q^{79} - 90q^{80} + 3q^{81} - 210q^{82} + 12q^{83} - 110q^{84} - 204q^{85} - 60q^{86} - 84q^{87} - 360q^{88} - 150q^{89} - 108q^{90} - 292q^{91} - 168q^{92} - 158q^{93} - 420q^{94} - 216q^{95} - 231q^{96} - 298q^{97} - 141q^{98} - 210q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)

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
507.2.a \(\chi_{507}(1, \cdot)\) 507.2.a.a 1 1
507.2.a.b 1
507.2.a.c 1
507.2.a.d 2
507.2.a.e 2
507.2.a.f 2
507.2.a.g 2
507.2.a.h 2
507.2.a.i 3
507.2.a.j 3
507.2.a.k 3
507.2.a.l 3
507.2.b \(\chi_{507}(337, \cdot)\) 507.2.b.a 2 1
507.2.b.b 2
507.2.b.c 2
507.2.b.d 4
507.2.b.e 4
507.2.b.f 6
507.2.b.g 6
507.2.e \(\chi_{507}(22, \cdot)\) 507.2.e.a 2 2
507.2.e.b 2
507.2.e.c 2
507.2.e.d 4
507.2.e.e 4
507.2.e.f 4
507.2.e.g 4
507.2.e.h 4
507.2.e.i 6
507.2.e.j 6
507.2.e.k 6
507.2.e.l 6
507.2.f \(\chi_{507}(239, \cdot)\) 507.2.f.a 4 2
507.2.f.b 4
507.2.f.c 4
507.2.f.d 8
507.2.f.e 8
507.2.f.f 8
507.2.f.g 48
507.2.j \(\chi_{507}(316, \cdot)\) 507.2.j.a 2 2
507.2.j.b 2
507.2.j.c 2
507.2.j.d 4
507.2.j.e 4
507.2.j.f 8
507.2.j.g 8
507.2.j.h 12
507.2.j.i 12
507.2.k \(\chi_{507}(80, \cdot)\) 507.2.k.a 4 4
507.2.k.b 4
507.2.k.c 4
507.2.k.d 8
507.2.k.e 8
507.2.k.f 8
507.2.k.g 8
507.2.k.h 8
507.2.k.i 8
507.2.k.j 8
507.2.k.k 96
507.2.m \(\chi_{507}(40, \cdot)\) 507.2.m.a 180 12
507.2.m.b 204
507.2.p \(\chi_{507}(25, \cdot)\) 507.2.p.a 168 12
507.2.p.b 192
507.2.q \(\chi_{507}(16, \cdot)\) 507.2.q.a 360 24
507.2.q.b 384
507.2.s \(\chi_{507}(5, \cdot)\) 507.2.s.a 1392 24
507.2.t \(\chi_{507}(4, \cdot)\) 507.2.t.a 336 24
507.2.t.b 360
507.2.x \(\chi_{507}(2, \cdot)\) 507.2.x.a 48 48
507.2.x.b 2784

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(507))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(507)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)