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Properties

Label 1690.2
Level 1690
Weight 2
Dimension 25717
Nonzero newspaces 24
Sturm bound 340704
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(340704\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1690))\).

Total New Old
Modular forms 87000 25717 61283
Cusp forms 83353 25717 57636
Eisenstein series 3647 0 3647

Trace form

\( 25717 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} + 8 q^{7} + 11 q^{8} + 51 q^{9} + O(q^{10}) \) \( 25717 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} + 8 q^{7} + 11 q^{8} + 51 q^{9} + 29 q^{10} + 36 q^{11} + 12 q^{12} + 48 q^{13} + 40 q^{14} + 44 q^{15} + 15 q^{16} + 42 q^{17} + 47 q^{18} + 92 q^{19} + 5 q^{20} + 80 q^{21} - 12 q^{22} + 24 q^{23} - 4 q^{24} - q^{25} + 104 q^{27} + 8 q^{28} + 126 q^{29} + 44 q^{30} + 128 q^{31} - q^{32} + 192 q^{33} + 78 q^{34} + 136 q^{35} + 83 q^{36} + 86 q^{37} + 124 q^{38} + 104 q^{39} - q^{40} + 162 q^{41} + 112 q^{42} + 132 q^{43} + 84 q^{44} + 137 q^{45} + 72 q^{46} + 144 q^{47} - 4 q^{48} + 71 q^{49} + 29 q^{50} + 24 q^{51} + 2 q^{52} - 102 q^{53} - 184 q^{54} - 180 q^{55} - 56 q^{56} - 304 q^{57} - 138 q^{58} - 156 q^{59} - 148 q^{60} - 98 q^{61} - 176 q^{62} - 280 q^{63} - 13 q^{64} - 105 q^{65} - 240 q^{66} - 148 q^{67} - 30 q^{68} - 288 q^{69} - 224 q^{70} + 24 q^{71} - 109 q^{72} - 10 q^{73} - 98 q^{74} - 228 q^{75} - 4 q^{76} + 96 q^{77} - 24 q^{78} + 112 q^{79} - 19 q^{80} + 183 q^{81} + 138 q^{82} + 300 q^{83} + 80 q^{84} + 228 q^{85} + 52 q^{86} + 360 q^{87} - 12 q^{88} + 294 q^{89} + 107 q^{90} + 152 q^{91} + 72 q^{92} + 320 q^{93} + 192 q^{94} + 124 q^{95} - 4 q^{96} + 302 q^{97} + 135 q^{98} + 276 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)

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
1690.2.a \(\chi_{1690}(1, \cdot)\) 1690.2.a.a 1 1
1690.2.a.b 1
1690.2.a.c 1
1690.2.a.d 1
1690.2.a.e 1
1690.2.a.f 1
1690.2.a.g 1
1690.2.a.h 1
1690.2.a.i 1
1690.2.a.j 2
1690.2.a.k 2
1690.2.a.l 2
1690.2.a.m 2
1690.2.a.n 2
1690.2.a.o 2
1690.2.a.p 3
1690.2.a.q 3
1690.2.a.r 3
1690.2.a.s 3
1690.2.a.t 4
1690.2.a.u 4
1690.2.a.v 6
1690.2.a.w 6
1690.2.b \(\chi_{1690}(339, \cdot)\) 1690.2.b.a 6 1
1690.2.b.b 6
1690.2.b.c 6
1690.2.b.d 8
1690.2.b.e 16
1690.2.b.f 18
1690.2.b.g 18
1690.2.c \(\chi_{1690}(1689, \cdot)\) 1690.2.c.a 6 1
1690.2.c.b 6
1690.2.c.c 6
1690.2.c.d 6
1690.2.c.e 8
1690.2.c.f 8
1690.2.c.g 18
1690.2.c.h 18
1690.2.d \(\chi_{1690}(1351, \cdot)\) 1690.2.d.a 2 1
1690.2.d.b 2
1690.2.d.c 2
1690.2.d.d 2
1690.2.d.e 2
1690.2.d.f 4
1690.2.d.g 4
1690.2.d.h 4
1690.2.d.i 6
1690.2.d.j 6
1690.2.d.k 8
1690.2.d.l 12
1690.2.e \(\chi_{1690}(191, \cdot)\) 1690.2.e.a 2 2
1690.2.e.b 2
1690.2.e.c 2
1690.2.e.d 2
1690.2.e.e 2
1690.2.e.f 2
1690.2.e.g 2
1690.2.e.h 2
1690.2.e.i 2
1690.2.e.j 2
1690.2.e.k 4
1690.2.e.l 4
1690.2.e.m 4
1690.2.e.n 4
1690.2.e.o 6
1690.2.e.p 6
1690.2.e.q 6
1690.2.e.r 6
1690.2.e.s 8
1690.2.e.t 8
1690.2.e.u 12
1690.2.e.v 12
1690.2.g \(\chi_{1690}(577, \cdot)\) n/a 154 2
1690.2.j \(\chi_{1690}(437, \cdot)\) n/a 154 2
1690.2.l \(\chi_{1690}(361, \cdot)\) 1690.2.l.a 4 2
1690.2.l.b 4
1690.2.l.c 4
1690.2.l.d 4
1690.2.l.e 4
1690.2.l.f 4
1690.2.l.g 4
1690.2.l.h 4
1690.2.l.i 4
1690.2.l.j 8
1690.2.l.k 8
1690.2.l.l 12
1690.2.l.m 12
1690.2.l.n 24
1690.2.m \(\chi_{1690}(699, \cdot)\) n/a 152 2
1690.2.n \(\chi_{1690}(529, \cdot)\) n/a 156 2
1690.2.p \(\chi_{1690}(427, \cdot)\) n/a 308 4
1690.2.s \(\chi_{1690}(357, \cdot)\) n/a 308 4
1690.2.u \(\chi_{1690}(131, \cdot)\) n/a 696 12
1690.2.v \(\chi_{1690}(51, \cdot)\) n/a 696 12
1690.2.w \(\chi_{1690}(129, \cdot)\) n/a 1104 12
1690.2.x \(\chi_{1690}(79, \cdot)\) n/a 1080 12
1690.2.y \(\chi_{1690}(61, \cdot)\) n/a 1488 24
1690.2.ba \(\chi_{1690}(47, \cdot)\) n/a 2184 24
1690.2.bd \(\chi_{1690}(57, \cdot)\) n/a 2184 24
1690.2.bf \(\chi_{1690}(9, \cdot)\) n/a 2160 24
1690.2.bg \(\chi_{1690}(49, \cdot)\) n/a 2208 24
1690.2.bh \(\chi_{1690}(101, \cdot)\) n/a 1488 24
1690.2.bj \(\chi_{1690}(33, \cdot)\) n/a 4368 48
1690.2.bm \(\chi_{1690}(7, \cdot)\) n/a 4368 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1690))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1690)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 2}\)