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Properties

Label 2002.2
Level 2002
Weight 2
Dimension 37537
Nonzero newspaces 60
Sturm bound 483840
Trace bound 14

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Defining parameters

Level: \( N \) = \( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(483840\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2002))\).

Total New Old
Modular forms 123840 37537 86303
Cusp forms 118081 37537 80544
Eisenstein series 5759 0 5759

Trace form

\( 37537 q - 7 q^{2} - 20 q^{3} + q^{4} - 18 q^{5} + 16 q^{6} + 29 q^{7} + 5 q^{8} + 109 q^{9} + O(q^{10}) \) \( 37537 q - 7 q^{2} - 20 q^{3} + q^{4} - 18 q^{5} + 16 q^{6} + 29 q^{7} + 5 q^{8} + 109 q^{9} + 82 q^{10} + 41 q^{11} + 36 q^{12} + 81 q^{13} + 37 q^{14} + 144 q^{15} + 17 q^{16} + 110 q^{17} + 37 q^{18} + 120 q^{19} - 6 q^{20} + 76 q^{21} - 23 q^{22} + 56 q^{23} + 16 q^{24} + 107 q^{25} + 21 q^{26} + 220 q^{27} + 29 q^{28} + 202 q^{29} + 144 q^{30} + 168 q^{31} + 13 q^{32} + 248 q^{33} + 98 q^{34} + 246 q^{35} + 81 q^{36} + 98 q^{37} + 196 q^{38} + 216 q^{39} + 22 q^{40} + 262 q^{41} + 128 q^{42} + 276 q^{43} + 85 q^{44} + 266 q^{45} + 104 q^{46} + 160 q^{47} - 20 q^{48} + 185 q^{49} + 115 q^{50} + 284 q^{51} + 33 q^{52} + 206 q^{53} + 168 q^{54} + 262 q^{55} + 17 q^{56} + 340 q^{57} + 202 q^{58} + 248 q^{59} + 104 q^{60} + 162 q^{61} + 64 q^{62} + 93 q^{63} + 13 q^{64} + 206 q^{65} - 236 q^{66} + 204 q^{67} - 58 q^{68} + 32 q^{69} - 226 q^{70} - 88 q^{71} - 107 q^{72} - 30 q^{73} - 270 q^{74} - 576 q^{75} - 212 q^{76} - 319 q^{77} - 332 q^{78} - 560 q^{79} - 86 q^{80} - 955 q^{81} - 622 q^{82} - 424 q^{83} - 460 q^{84} - 736 q^{85} - 456 q^{86} - 896 q^{87} - 103 q^{88} - 406 q^{89} - 834 q^{90} - 587 q^{91} - 144 q^{92} - 368 q^{93} - 456 q^{94} - 328 q^{95} - 4 q^{96} - 418 q^{97} - 179 q^{98} + 5 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2002))\)

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
2002.2.a \(\chi_{2002}(1, \cdot)\) 2002.2.a.a 1 1
2002.2.a.b 1
2002.2.a.c 1
2002.2.a.d 2
2002.2.a.e 2
2002.2.a.f 2
2002.2.a.g 2
2002.2.a.h 2
2002.2.a.i 3
2002.2.a.j 3
2002.2.a.k 3
2002.2.a.l 4
2002.2.a.m 4
2002.2.a.n 5
2002.2.a.o 5
2002.2.a.p 5
2002.2.a.q 5
2002.2.a.r 5
2002.2.a.s 6
2002.2.c \(\chi_{2002}(1847, \cdot)\) 2002.2.c.a 48 1
2002.2.c.b 48
2002.2.e \(\chi_{2002}(2001, \cdot)\) n/a 112 1
2002.2.g \(\chi_{2002}(155, \cdot)\) 2002.2.g.a 12 1
2002.2.g.b 18
2002.2.g.c 18
2002.2.g.d 20
2002.2.i \(\chi_{2002}(529, \cdot)\) n/a 184 2
2002.2.j \(\chi_{2002}(1145, \cdot)\) n/a 160 2
2002.2.k \(\chi_{2002}(1387, \cdot)\) n/a 144 2
2002.2.l \(\chi_{2002}(991, \cdot)\) n/a 184 2
2002.2.n \(\chi_{2002}(265, \cdot)\) n/a 176 2
2002.2.p \(\chi_{2002}(967, \cdot)\) n/a 168 2
2002.2.q \(\chi_{2002}(729, \cdot)\) n/a 288 4
2002.2.r \(\chi_{2002}(901, \cdot)\) n/a 224 2
2002.2.t \(\chi_{2002}(549, \cdot)\) n/a 224 2
2002.2.v \(\chi_{2002}(309, \cdot)\) n/a 136 2
2002.2.z \(\chi_{2002}(1299, \cdot)\) n/a 192 2
2002.2.bc \(\chi_{2002}(23, \cdot)\) n/a 184 2
2002.2.be \(\chi_{2002}(1231, \cdot)\) n/a 224 2
2002.2.bg \(\chi_{2002}(285, \cdot)\) n/a 224 2
2002.2.bj \(\chi_{2002}(439, \cdot)\) n/a 224 2
2002.2.bl \(\chi_{2002}(87, \cdot)\) n/a 224 2
2002.2.bm \(\chi_{2002}(131, \cdot)\) n/a 192 2
2002.2.bo \(\chi_{2002}(153, \cdot)\) n/a 224 2
2002.2.br \(\chi_{2002}(485, \cdot)\) n/a 184 2
2002.2.bu \(\chi_{2002}(883, \cdot)\) n/a 336 4
2002.2.bw \(\chi_{2002}(545, \cdot)\) n/a 448 4
2002.2.by \(\chi_{2002}(391, \cdot)\) n/a 384 4
2002.2.ca \(\chi_{2002}(353, \cdot)\) n/a 368 4
2002.2.cd \(\chi_{2002}(197, \cdot)\) n/a 336 4
2002.2.ce \(\chi_{2002}(109, \cdot)\) n/a 448 4
2002.2.ch \(\chi_{2002}(219, \cdot)\) n/a 448 4
2002.2.cj \(\chi_{2002}(111, \cdot)\) n/a 384 4
2002.2.ck \(\chi_{2002}(551, \cdot)\) n/a 384 4
2002.2.cn \(\chi_{2002}(45, \cdot)\) n/a 368 4
2002.2.co \(\chi_{2002}(527, \cdot)\) n/a 448 4
2002.2.cq \(\chi_{2002}(9, \cdot)\) n/a 896 8
2002.2.cr \(\chi_{2002}(113, \cdot)\) n/a 672 8
2002.2.cs \(\chi_{2002}(53, \cdot)\) n/a 768 8
2002.2.ct \(\chi_{2002}(289, \cdot)\) n/a 896 8
2002.2.cu \(\chi_{2002}(57, \cdot)\) n/a 672 8
2002.2.cw \(\chi_{2002}(125, \cdot)\) n/a 896 8
2002.2.cz \(\chi_{2002}(179, \cdot)\) n/a 896 8
2002.2.dc \(\chi_{2002}(699, \cdot)\) n/a 896 8
2002.2.de \(\chi_{2002}(677, \cdot)\) n/a 768 8
2002.2.df \(\chi_{2002}(523, \cdot)\) n/a 896 8
2002.2.dh \(\chi_{2002}(17, \cdot)\) n/a 896 8
2002.2.dk \(\chi_{2002}(129, \cdot)\) n/a 896 8
2002.2.dm \(\chi_{2002}(139, \cdot)\) n/a 896 8
2002.2.do \(\chi_{2002}(641, \cdot)\) n/a 896 8
2002.2.dr \(\chi_{2002}(25, \cdot)\) n/a 896 8
2002.2.dv \(\chi_{2002}(225, \cdot)\) n/a 672 8
2002.2.dx \(\chi_{2002}(61, \cdot)\) n/a 896 8
2002.2.dz \(\chi_{2002}(101, \cdot)\) n/a 896 8
2002.2.eb \(\chi_{2002}(149, \cdot)\) n/a 1792 16
2002.2.ec \(\chi_{2002}(59, \cdot)\) n/a 1792 16
2002.2.ef \(\chi_{2002}(5, \cdot)\) n/a 1792 16
2002.2.eg \(\chi_{2002}(97, \cdot)\) n/a 1792 16
2002.2.ei \(\chi_{2002}(123, \cdot)\) n/a 1792 16
2002.2.el \(\chi_{2002}(151, \cdot)\) n/a 1792 16
2002.2.em \(\chi_{2002}(85, \cdot)\) n/a 1344 16
2002.2.ep \(\chi_{2002}(115, \cdot)\) n/a 1792 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 2}\)