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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

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

Display 100 coefficients 10 coefficients

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 available 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

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