↑

Properties

Label 417.2
Level 417
Weight 2
Dimension 4691
Nonzero newspaces 8
Newform subspaces 20
Sturm bound 25760
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 417 = 3 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 20 \)
Sturm bound: \(25760\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(417))\).

Total New Old
Modular forms 6716 4967 1749
Cusp forms 6165 4691 1474
Eisenstein series 551 276 275

Trace form

\( 4691 q - 3 q^{2} - 70 q^{3} - 145 q^{4} - 6 q^{5} - 72 q^{6} - 146 q^{7} - 15 q^{8} - 70 q^{9} + O(q^{10}) \) \( 4691 q - 3 q^{2} - 70 q^{3} - 145 q^{4} - 6 q^{5} - 72 q^{6} - 146 q^{7} - 15 q^{8} - 70 q^{9} - 156 q^{10} - 12 q^{11} - 76 q^{12} - 152 q^{13} - 24 q^{14} - 75 q^{15} - 169 q^{16} - 18 q^{17} - 72 q^{18} - 158 q^{19} - 42 q^{20} - 77 q^{21} - 174 q^{22} - 24 q^{23} - 84 q^{24} - 169 q^{25} - 42 q^{26} - 70 q^{27} - 194 q^{28} - 30 q^{29} - 87 q^{30} - 170 q^{31} - 63 q^{32} - 81 q^{33} - 192 q^{34} - 48 q^{35} - 76 q^{36} - 176 q^{37} - 60 q^{38} - 83 q^{39} - 228 q^{40} - 42 q^{41} - 93 q^{42} - 182 q^{43} - 84 q^{44} - 75 q^{45} - 210 q^{46} - 48 q^{47} - 100 q^{48} - 195 q^{49} - 93 q^{50} - 87 q^{51} - 236 q^{52} - 54 q^{53} - 72 q^{54} - 210 q^{55} - 120 q^{56} - 89 q^{57} - 228 q^{58} - 60 q^{59} - 111 q^{60} - 200 q^{61} - 96 q^{62} - 77 q^{63} - 265 q^{64} - 84 q^{65} - 105 q^{66} - 206 q^{67} - 126 q^{68} - 93 q^{69} - 282 q^{70} - 72 q^{71} - 84 q^{72} - 212 q^{73} - 114 q^{74} - 100 q^{75} - 278 q^{76} - 96 q^{77} - 111 q^{78} - 218 q^{79} - 186 q^{80} - 70 q^{81} - 264 q^{82} - 84 q^{83} - 125 q^{84} - 246 q^{85} - 132 q^{86} - 99 q^{87} - 318 q^{88} - 90 q^{89} - 87 q^{90} - 250 q^{91} - 168 q^{92} - 101 q^{93} - 282 q^{94} - 120 q^{95} - 132 q^{96} - 236 q^{97} - 171 q^{98} - 81 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(417))\)

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
417.2.a \(\chi_{417}(1, \cdot)\) 417.2.a.a 1 1
417.2.a.b 2
417.2.a.c 3
417.2.a.d 3
417.2.a.e 7
417.2.a.f 7
417.2.d \(\chi_{417}(416, \cdot)\) 417.2.d.a 16 1
417.2.d.b 28
417.2.e \(\chi_{417}(181, \cdot)\) 417.2.e.a 2 2
417.2.e.b 20
417.2.e.c 24
417.2.f \(\chi_{417}(182, \cdot)\) 417.2.f.a 2 2
417.2.f.b 88
417.2.i \(\chi_{417}(34, \cdot)\) 417.2.i.a 242 22
417.2.i.b 286
417.2.j \(\chi_{417}(8, \cdot)\) 417.2.j.a 968 22
417.2.m \(\chi_{417}(4, \cdot)\) 417.2.m.a 484 44
417.2.m.b 528
417.2.p \(\chi_{417}(2, \cdot)\) 417.2.p.a 44 44
417.2.p.b 1936

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(417))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(417)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(139))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(417))\)\(^{\oplus 1}\)