# Properties

 Label 2001.2 Level 2001 Weight 2 Dimension 109067 Nonzero newspaces 24 Sturm bound 591360 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$591360$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2001))$$.

Total New Old
Modular forms 150304 111331 38973
Cusp forms 145377 109067 36310
Eisenstein series 4927 2264 2663

## Trace form

 $$109067q + 9q^{2} - 255q^{3} - 495q^{4} + 18q^{5} - 249q^{6} - 492q^{7} + 45q^{8} - 255q^{9} + O(q^{10})$$ $$109067q + 9q^{2} - 255q^{3} - 495q^{4} + 18q^{5} - 249q^{6} - 492q^{7} + 45q^{8} - 255q^{9} - 462q^{10} + 36q^{11} - 237q^{12} - 474q^{13} + 72q^{14} - 262q^{15} - 511q^{16} + 10q^{17} - 337q^{18} - 500q^{19} - 134q^{20} - 356q^{21} - 652q^{22} - 69q^{23} - 799q^{24} - 623q^{25} - 102q^{26} - 405q^{27} - 804q^{28} - 75q^{29} - 740q^{30} - 576q^{31} - 123q^{32} - 328q^{33} - 582q^{34} - 56q^{35} - 449q^{36} - 634q^{37} - 152q^{38} - 360q^{39} - 682q^{40} + 38q^{41} - 406q^{42} - 560q^{43} - 112q^{44} - 290q^{45} - 895q^{46} - 144q^{47} - 609q^{48} - 833q^{49} - 421q^{50} - 404q^{51} - 1110q^{52} - 178q^{53} - 249q^{54} - 924q^{55} - 252q^{56} - 360q^{57} - 1143q^{58} - 20q^{59} - 348q^{60} - 554q^{61} - 104q^{62} - 180q^{63} - 639q^{64} - 264q^{66} - 536q^{67} - 14q^{68} - 171q^{69} - 1104q^{70} + 104q^{71} + 163q^{72} - 434q^{73} + 242q^{74} + 41q^{75} - 316q^{76} + 112q^{77} + 4q^{78} - 452q^{79} + 162q^{80} - 207q^{81} - 402q^{82} + 76q^{83} - 14q^{84} - 632q^{85} - 44q^{86} - 202q^{87} - 1064q^{88} + 6q^{89} - 298q^{90} - 576q^{91} - 67q^{92} - 600q^{93} - 568q^{94} - 36q^{95} - 179q^{96} - 814q^{97} - 295q^{98} - 614q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2001))$$

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
2001.2.a $$\chi_{2001}(1, \cdot)$$ 2001.2.a.a 1 1
2001.2.a.b 1
2001.2.a.c 1
2001.2.a.d 2
2001.2.a.e 2
2001.2.a.f 2
2001.2.a.g 4
2001.2.a.h 5
2001.2.a.i 7
2001.2.a.j 7
2001.2.a.k 10
2001.2.a.l 11
2001.2.a.m 14
2001.2.a.n 16
2001.2.a.o 20
2001.2.d $$\chi_{2001}(1103, \cdot)$$ n/a 224 1
2001.2.e $$\chi_{2001}(898, \cdot)$$ n/a 112 1
2001.2.h $$\chi_{2001}(2000, \cdot)$$ n/a 236 1
2001.2.k $$\chi_{2001}(505, \cdot)$$ n/a 240 2
2001.2.l $$\chi_{2001}(737, \cdot)$$ n/a 440 2
2001.2.m $$\chi_{2001}(139, \cdot)$$ n/a 648 6
2001.2.n $$\chi_{2001}(262, \cdot)$$ n/a 1120 10
2001.2.o $$\chi_{2001}(689, \cdot)$$ n/a 1416 6
2001.2.r $$\chi_{2001}(208, \cdot)$$ n/a 672 6
2001.2.s $$\chi_{2001}(344, \cdot)$$ n/a 1416 6
2001.2.v $$\chi_{2001}(86, \cdot)$$ n/a 2360 10
2001.2.y $$\chi_{2001}(202, \cdot)$$ n/a 1200 10
2001.2.z $$\chi_{2001}(320, \cdot)$$ n/a 2240 10
2001.2.bc $$\chi_{2001}(47, \cdot)$$ n/a 2640 12
2001.2.bd $$\chi_{2001}(160, \cdot)$$ n/a 1440 12
2001.2.bg $$\chi_{2001}(41, \cdot)$$ n/a 4720 20
2001.2.bh $$\chi_{2001}(157, \cdot)$$ n/a 2400 20
2001.2.bk $$\chi_{2001}(16, \cdot)$$ n/a 7200 60
2001.2.bn $$\chi_{2001}(20, \cdot)$$ n/a 14160 60
2001.2.bo $$\chi_{2001}(4, \cdot)$$ n/a 7200 60
2001.2.br $$\chi_{2001}(5, \cdot)$$ n/a 14160 60
2001.2.bu $$\chi_{2001}(10, \cdot)$$ n/a 14400 120
2001.2.bv $$\chi_{2001}(2, \cdot)$$ n/a 28320 120

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2001))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2001)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(667))$$$$^{\oplus 2}$$