# Properties

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

## 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

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