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Properties

Label 1682.2
Level 1682
Weight 2
Dimension 29366
Nonzero newspaces 8
Sturm bound 353220
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1682 = 2 \cdot 29^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(353220\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1682))\).

Total New Old
Modular forms 89509 29366 60143
Cusp forms 87102 29366 57736
Eisenstein series 2407 0 2407

Trace form

\( 29366 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 29366 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 24 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} - 8 q^{20} - 80 q^{21} - 44 q^{22} - 32 q^{23} - 52 q^{24} - 81 q^{25} - 56 q^{26} - 128 q^{27} + 8 q^{28} - 56 q^{29} - 144 q^{30} - 80 q^{31} + q^{32} - 120 q^{33} - 52 q^{34} - 64 q^{35} - 43 q^{36} - 18 q^{37} - 36 q^{38} - 56 q^{39} - 8 q^{40} + 42 q^{41} + 32 q^{42} + 44 q^{43} + 12 q^{44} + 8 q^{45} + 24 q^{46} - 8 q^{47} + 4 q^{48} - 55 q^{49} + 31 q^{50} - 40 q^{51} + 14 q^{52} - 72 q^{53} + 40 q^{54} - 152 q^{55} + 8 q^{56} - 32 q^{57} + 4 q^{59} + 24 q^{60} - 50 q^{61} + 32 q^{62} - 120 q^{63} + q^{64} - 42 q^{65} + 48 q^{66} - 44 q^{67} + 18 q^{68} - 16 q^{69} - 8 q^{70} - 152 q^{71} + 13 q^{72} - 108 q^{73} - 130 q^{74} - 156 q^{75} - 92 q^{76} - 184 q^{77} - 168 q^{78} - 32 q^{79} + 6 q^{80} - 327 q^{81} - 70 q^{82} - 140 q^{83} - 136 q^{84} - 228 q^{85} - 236 q^{86} - 140 q^{87} + 12 q^{88} - 190 q^{89} - 202 q^{90} - 224 q^{91} - 144 q^{92} - 96 q^{93} - 64 q^{94} - 328 q^{95} + 4 q^{96} - 28 q^{97} - 167 q^{98} - 236 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)

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
1682.2.a \(\chi_{1682}(1, \cdot)\) 1682.2.a.a 1 1
1682.2.a.b 1
1682.2.a.c 1
1682.2.a.d 1
1682.2.a.e 1
1682.2.a.f 1
1682.2.a.g 1
1682.2.a.h 1
1682.2.a.i 1
1682.2.a.j 1
1682.2.a.k 2
1682.2.a.l 2
1682.2.a.m 3
1682.2.a.n 3
1682.2.a.o 4
1682.2.a.p 4
1682.2.a.q 6
1682.2.a.r 6
1682.2.a.s 6
1682.2.a.t 6
1682.2.a.u 8
1682.2.a.v 8
1682.2.b \(\chi_{1682}(1681, \cdot)\) 1682.2.b.a 2 1
1682.2.b.b 2
1682.2.b.c 2
1682.2.b.d 2
1682.2.b.e 2
1682.2.b.f 4
1682.2.b.g 6
1682.2.b.h 8
1682.2.b.i 12
1682.2.b.j 12
1682.2.b.k 16
1682.2.d \(\chi_{1682}(571, \cdot)\) n/a 402 6
1682.2.e \(\chi_{1682}(63, \cdot)\) n/a 408 6
1682.2.g \(\chi_{1682}(59, \cdot)\) n/a 2044 28
1682.2.h \(\chi_{1682}(57, \cdot)\) n/a 2016 28
1682.2.j \(\chi_{1682}(7, \cdot)\) n/a 12264 168
1682.2.k \(\chi_{1682}(5, \cdot)\) n/a 12096 168

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1682))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1682)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)