Properties

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

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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

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