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

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

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 the 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

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