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Properties

Label 1610.2
Level 1610
Weight 2
Dimension 22173
Nonzero newspaces 24
Sturm bound 304128
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(304128\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1610))\).

Total New Old
Modular forms 78144 22173 55971
Cusp forms 73921 22173 51748
Eisenstein series 4223 0 4223

Trace form

\( 22173 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 9 q^{5} + 12 q^{6} + 17 q^{7} - 3 q^{8} + 17 q^{9} + O(q^{10}) \) \( 22173 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 9 q^{5} + 12 q^{6} + 17 q^{7} - 3 q^{8} + 17 q^{9} + 9 q^{10} + 12 q^{11} - 4 q^{12} - 2 q^{13} + 9 q^{14} + 80 q^{15} + 5 q^{16} + 130 q^{17} + 185 q^{18} + 116 q^{19} + 53 q^{20} + 176 q^{21} + 100 q^{22} + 177 q^{23} + 12 q^{24} + 69 q^{25} + 70 q^{26} + 176 q^{27} + 13 q^{28} - 2 q^{29} - 20 q^{30} + 8 q^{31} - 3 q^{32} - 104 q^{33} - 102 q^{34} - 53 q^{35} - 79 q^{36} + 78 q^{37} - 84 q^{38} + 24 q^{39} + 9 q^{40} + 58 q^{41} - 84 q^{42} + 156 q^{43} - 36 q^{44} + 105 q^{45} - 23 q^{46} + 128 q^{47} - 4 q^{48} + 233 q^{49} + 69 q^{50} + 200 q^{51} - 2 q^{52} + 166 q^{53} + 112 q^{54} + 236 q^{55} + 53 q^{56} + 408 q^{57} + 230 q^{58} + 380 q^{59} + 80 q^{60} + 302 q^{61} + 312 q^{62} + 201 q^{63} + 5 q^{64} + 290 q^{65} + 400 q^{66} + 36 q^{67} + 218 q^{68} + 348 q^{69} + 157 q^{70} + 416 q^{71} + 185 q^{72} + 66 q^{73} + 382 q^{74} + 396 q^{75} + 28 q^{76} + 232 q^{77} + 288 q^{78} + 360 q^{79} + 53 q^{80} + 461 q^{81} + 194 q^{82} + 316 q^{83} + 88 q^{84} + 198 q^{85} + 52 q^{86} + 240 q^{87} - 36 q^{88} - 86 q^{89} - 75 q^{90} + 62 q^{91} - 47 q^{92} - 176 q^{93} - 96 q^{94} - 248 q^{95} - 36 q^{96} - 406 q^{97} - 283 q^{98} - 404 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1610))\)

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
1610.2.a \(\chi_{1610}(1, \cdot)\) 1610.2.a.a 1 1
1610.2.a.b 1
1610.2.a.c 1
1610.2.a.d 1
1610.2.a.e 1
1610.2.a.f 1
1610.2.a.g 1
1610.2.a.h 2
1610.2.a.i 2
1610.2.a.j 2
1610.2.a.k 3
1610.2.a.l 3
1610.2.a.m 3
1610.2.a.n 3
1610.2.a.o 3
1610.2.a.p 4
1610.2.a.q 4
1610.2.a.r 4
1610.2.a.s 5
1610.2.c \(\chi_{1610}(321, \cdot)\) 1610.2.c.a 4 1
1610.2.c.b 4
1610.2.c.c 4
1610.2.c.d 4
1610.2.c.e 12
1610.2.c.f 12
1610.2.c.g 12
1610.2.c.h 12
1610.2.e \(\chi_{1610}(1289, \cdot)\) 1610.2.e.a 10 1
1610.2.e.b 14
1610.2.e.c 18
1610.2.e.d 22
1610.2.g \(\chi_{1610}(1609, \cdot)\) 1610.2.g.a 96 1
1610.2.i \(\chi_{1610}(921, \cdot)\) n/a 112 2
1610.2.k \(\chi_{1610}(183, \cdot)\) n/a 144 2
1610.2.m \(\chi_{1610}(783, \cdot)\) n/a 176 2
1610.2.o \(\chi_{1610}(229, \cdot)\) n/a 192 2
1610.2.q \(\chi_{1610}(599, \cdot)\) n/a 176 2
1610.2.s \(\chi_{1610}(551, \cdot)\) n/a 128 2
1610.2.u \(\chi_{1610}(71, \cdot)\) n/a 480 10
1610.2.v \(\chi_{1610}(47, \cdot)\) n/a 352 4
1610.2.x \(\chi_{1610}(137, \cdot)\) n/a 384 4
1610.2.ba \(\chi_{1610}(419, \cdot)\) n/a 960 10
1610.2.bc \(\chi_{1610}(29, \cdot)\) n/a 720 10
1610.2.be \(\chi_{1610}(111, \cdot)\) n/a 640 10
1610.2.bg \(\chi_{1610}(81, \cdot)\) n/a 1280 20
1610.2.bh \(\chi_{1610}(13, \cdot)\) n/a 1920 20
1610.2.bj \(\chi_{1610}(43, \cdot)\) n/a 1440 20
1610.2.bm \(\chi_{1610}(61, \cdot)\) n/a 1280 20
1610.2.bo \(\chi_{1610}(9, \cdot)\) n/a 1920 20
1610.2.bq \(\chi_{1610}(19, \cdot)\) n/a 1920 20
1610.2.bt \(\chi_{1610}(37, \cdot)\) n/a 3840 40
1610.2.bv \(\chi_{1610}(3, \cdot)\) n/a 3840 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 2}\)