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Properties

Label 1001.2
Level 1001
Weight 2
Dimension 36559
Nonzero newspaces 60
Sturm bound 161280
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(161280\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1001))\).

Total New Old
Modular forms 41760 38535 3225
Cusp forms 38881 36559 2322
Eisenstein series 2879 1976 903

Trace form

\( 36559 q - 143 q^{2} - 140 q^{3} - 131 q^{4} - 134 q^{5} - 136 q^{6} - 201 q^{7} - 411 q^{8} - 185 q^{9} + O(q^{10}) \) \( 36559 q - 143 q^{2} - 140 q^{3} - 131 q^{4} - 134 q^{5} - 136 q^{6} - 201 q^{7} - 411 q^{8} - 185 q^{9} - 218 q^{10} - 185 q^{11} - 452 q^{12} - 203 q^{13} - 475 q^{14} - 436 q^{15} - 259 q^{16} - 194 q^{17} - 287 q^{18} - 232 q^{19} - 298 q^{20} - 280 q^{21} - 551 q^{22} - 388 q^{23} - 432 q^{24} - 263 q^{25} - 301 q^{26} - 488 q^{27} - 379 q^{28} - 498 q^{29} - 484 q^{30} - 240 q^{31} - 427 q^{32} - 328 q^{33} - 542 q^{34} - 346 q^{35} - 803 q^{36} - 226 q^{37} - 360 q^{38} - 302 q^{39} - 702 q^{40} - 386 q^{41} - 524 q^{42} - 612 q^{43} - 451 q^{44} - 698 q^{45} - 532 q^{46} - 316 q^{47} - 672 q^{48} - 413 q^{49} - 793 q^{50} - 508 q^{51} - 485 q^{52} - 594 q^{53} - 700 q^{54} - 410 q^{55} - 843 q^{56} - 736 q^{57} - 522 q^{58} - 340 q^{59} - 596 q^{60} - 314 q^{61} - 500 q^{62} - 357 q^{63} - 771 q^{64} - 394 q^{65} - 400 q^{66} - 512 q^{67} - 406 q^{68} - 236 q^{69} - 322 q^{70} - 444 q^{71} + 81 q^{72} - 258 q^{73} - 378 q^{74} - 80 q^{75} + 212 q^{76} - 169 q^{77} - 1124 q^{78} - 216 q^{79} + 62 q^{80} + 127 q^{81} + 178 q^{82} - 156 q^{83} + 420 q^{84} - 176 q^{85} - 72 q^{86} - 27 q^{88} - 318 q^{89} + 34 q^{90} - 97 q^{91} - 776 q^{92} - 332 q^{93} - 76 q^{94} - 336 q^{95} - 56 q^{96} - 146 q^{97} - 347 q^{98} - 785 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)

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
1001.2.a \(\chi_{1001}(1, \cdot)\) 1001.2.a.a 1 1
1001.2.a.b 1
1001.2.a.c 1
1001.2.a.d 2
1001.2.a.e 2
1001.2.a.f 3
1001.2.a.g 4
1001.2.a.h 4
1001.2.a.i 5
1001.2.a.j 5
1001.2.a.k 5
1001.2.a.l 7
1001.2.a.m 8
1001.2.a.n 11
1001.2.b \(\chi_{1001}(846, \cdot)\) 1001.2.b.a 48 1
1001.2.b.b 48
1001.2.d \(\chi_{1001}(155, \cdot)\) 1001.2.d.a 2 1
1001.2.d.b 30
1001.2.d.c 40
1001.2.g \(\chi_{1001}(1000, \cdot)\) n/a 108 1
1001.2.i \(\chi_{1001}(144, \cdot)\) 1001.2.i.a 8 2
1001.2.i.b 22
1001.2.i.c 30
1001.2.i.d 50
1001.2.i.e 50
1001.2.j \(\chi_{1001}(386, \cdot)\) n/a 136 2
1001.2.k \(\chi_{1001}(100, \cdot)\) n/a 188 2
1001.2.l \(\chi_{1001}(529, \cdot)\) n/a 188 2
1001.2.n \(\chi_{1001}(34, \cdot)\) n/a 192 2
1001.2.p \(\chi_{1001}(736, \cdot)\) n/a 168 2
1001.2.q \(\chi_{1001}(92, \cdot)\) n/a 288 4
1001.2.s \(\chi_{1001}(23, \cdot)\) n/a 188 2
1001.2.u \(\chi_{1001}(87, \cdot)\) n/a 216 2
1001.2.v \(\chi_{1001}(10, \cdot)\) n/a 216 2
1001.2.ba \(\chi_{1001}(285, \cdot)\) n/a 216 2
1001.2.bc \(\chi_{1001}(153, \cdot)\) n/a 216 2
1001.2.bf \(\chi_{1001}(516, \cdot)\) n/a 216 2
1001.2.bg \(\chi_{1001}(309, \cdot)\) n/a 144 2
1001.2.bi \(\chi_{1001}(298, \cdot)\) n/a 184 2
1001.2.bk \(\chi_{1001}(230, \cdot)\) n/a 216 2
1001.2.bm \(\chi_{1001}(131, \cdot)\) n/a 192 2
1001.2.bp \(\chi_{1001}(452, \cdot)\) n/a 188 2
1001.2.br \(\chi_{1001}(439, \cdot)\) n/a 216 2
1001.2.bu \(\chi_{1001}(90, \cdot)\) n/a 432 4
1001.2.bx \(\chi_{1001}(64, \cdot)\) n/a 336 4
1001.2.bz \(\chi_{1001}(118, \cdot)\) n/a 384 4
1001.2.cb \(\chi_{1001}(353, \cdot)\) n/a 376 4
1001.2.cc \(\chi_{1001}(32, \cdot)\) n/a 432 4
1001.2.ce \(\chi_{1001}(197, \cdot)\) n/a 336 4
1001.2.cf \(\chi_{1001}(109, \cdot)\) n/a 432 4
1001.2.ci \(\chi_{1001}(45, \cdot)\) n/a 376 4
1001.2.ck \(\chi_{1001}(122, \cdot)\) n/a 368 4
1001.2.cl \(\chi_{1001}(111, \cdot)\) n/a 368 4
1001.2.cp \(\chi_{1001}(340, \cdot)\) n/a 432 4
1001.2.cq \(\chi_{1001}(16, \cdot)\) n/a 864 8
1001.2.cr \(\chi_{1001}(9, \cdot)\) n/a 864 8
1001.2.cs \(\chi_{1001}(113, \cdot)\) n/a 672 8
1001.2.ct \(\chi_{1001}(53, \cdot)\) n/a 768 8
1001.2.cv \(\chi_{1001}(8, \cdot)\) n/a 672 8
1001.2.cx \(\chi_{1001}(125, \cdot)\) n/a 864 8
1001.2.cz \(\chi_{1001}(17, \cdot)\) n/a 864 8
1001.2.db \(\chi_{1001}(179, \cdot)\) n/a 864 8
1001.2.de \(\chi_{1001}(40, \cdot)\) n/a 768 8
1001.2.dg \(\chi_{1001}(139, \cdot)\) n/a 864 8
1001.2.di \(\chi_{1001}(25, \cdot)\) n/a 864 8
1001.2.dk \(\chi_{1001}(36, \cdot)\) n/a 672 8
1001.2.dl \(\chi_{1001}(61, \cdot)\) n/a 864 8
1001.2.do \(\chi_{1001}(62, \cdot)\) n/a 864 8
1001.2.dq \(\chi_{1001}(129, \cdot)\) n/a 864 8
1001.2.dv \(\chi_{1001}(101, \cdot)\) n/a 864 8
1001.2.dw \(\chi_{1001}(68, \cdot)\) n/a 864 8
1001.2.dy \(\chi_{1001}(4, \cdot)\) n/a 864 8
1001.2.eb \(\chi_{1001}(72, \cdot)\) n/a 1728 16
1001.2.ec \(\chi_{1001}(5, \cdot)\) n/a 1728 16
1001.2.ed \(\chi_{1001}(20, \cdot)\) n/a 1728 16
1001.2.eg \(\chi_{1001}(59, \cdot)\) n/a 1728 16
1001.2.ei \(\chi_{1001}(50, \cdot)\) n/a 1344 16
1001.2.ej \(\chi_{1001}(18, \cdot)\) n/a 1728 16
1001.2.em \(\chi_{1001}(2, \cdot)\) n/a 1728 16
1001.2.ep \(\chi_{1001}(80, \cdot)\) n/a 1728 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1001))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)