Properties

Label 2900.2
Level 2900
Weight 2
Dimension 134055
Nonzero newspaces 40
Sturm bound 1008000
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1008000\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2900))\).

Total New Old
Modular forms 255920 136271 119649
Cusp forms 248081 134055 114026
Eisenstein series 7839 2216 5623

Trace form

\( 134055 q - 170 q^{2} - 8 q^{3} - 162 q^{4} - 418 q^{5} - 258 q^{6} + 8 q^{7} - 146 q^{8} - 320 q^{9} + O(q^{10}) \) \( 134055 q - 170 q^{2} - 8 q^{3} - 162 q^{4} - 418 q^{5} - 258 q^{6} + 8 q^{7} - 146 q^{8} - 320 q^{9} - 192 q^{10} - 162 q^{12} - 324 q^{13} - 162 q^{14} + 4 q^{15} - 290 q^{16} - 304 q^{17} - 186 q^{18} + 24 q^{19} - 212 q^{20} - 520 q^{21} - 162 q^{22} + 50 q^{23} - 182 q^{24} - 334 q^{25} - 502 q^{26} + 34 q^{27} - 148 q^{28} - 340 q^{29} - 428 q^{30} - 4 q^{31} - 130 q^{32} - 326 q^{33} - 162 q^{34} + 16 q^{35} - 274 q^{36} - 396 q^{37} - 222 q^{38} - 124 q^{39} - 312 q^{40} - 596 q^{41} - 362 q^{42} - 120 q^{43} - 288 q^{44} - 558 q^{45} - 308 q^{46} - 76 q^{47} - 310 q^{48} - 410 q^{49} - 412 q^{50} - 16 q^{51} - 246 q^{52} - 303 q^{53} - 296 q^{54} - 80 q^{55} - 280 q^{56} - 368 q^{57} - 58 q^{58} + 16 q^{59} - 404 q^{60} - 356 q^{61} - 164 q^{62} + 140 q^{63} - 96 q^{64} - 318 q^{65} - 242 q^{66} + 144 q^{67} - 112 q^{68} - 176 q^{69} - 204 q^{70} + 18 q^{71} - 80 q^{72} - 317 q^{73} - 168 q^{74} + 156 q^{75} - 454 q^{76} - 234 q^{77} - 222 q^{78} + 84 q^{79} - 172 q^{80} - 808 q^{81} - 18 q^{82} + 68 q^{83} - 44 q^{84} - 502 q^{85} - 124 q^{86} - 84 q^{87} - 104 q^{88} - 588 q^{89} + 108 q^{90} - 108 q^{91} + 38 q^{92} - 568 q^{93} + 158 q^{94} - 72 q^{95} - 100 q^{96} - 603 q^{97} + 64 q^{98} - 134 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2900))\)

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
2900.2.a \(\chi_{2900}(1, \cdot)\) 2900.2.a.a 1 1
2900.2.a.b 1
2900.2.a.c 1
2900.2.a.d 1
2900.2.a.e 1
2900.2.a.f 3
2900.2.a.g 3
2900.2.a.h 4
2900.2.a.i 5
2900.2.a.j 5
2900.2.a.k 5
2900.2.a.l 5
2900.2.a.m 10
2900.2.c \(\chi_{2900}(349, \cdot)\) 2900.2.c.a 2 1
2900.2.c.b 2
2900.2.c.c 2
2900.2.c.d 2
2900.2.c.e 2
2900.2.c.f 6
2900.2.c.g 6
2900.2.c.h 10
2900.2.c.i 10
2900.2.d \(\chi_{2900}(1101, \cdot)\) 2900.2.d.a 2 1
2900.2.d.b 2
2900.2.d.c 4
2900.2.d.d 4
2900.2.d.e 10
2900.2.d.f 10
2900.2.d.g 16
2900.2.f \(\chi_{2900}(1449, \cdot)\) 2900.2.f.a 4 1
2900.2.f.b 4
2900.2.f.c 8
2900.2.f.d 8
2900.2.f.e 20
2900.2.j \(\chi_{2900}(1757, \cdot)\) 2900.2.j.a 2 2
2900.2.j.b 2
2900.2.j.c 16
2900.2.j.d 30
2900.2.j.e 40
2900.2.k \(\chi_{2900}(1351, \cdot)\) n/a 558 2
2900.2.n \(\chi_{2900}(407, \cdot)\) n/a 504 2
2900.2.o \(\chi_{2900}(1043, \cdot)\) n/a 532 2
2900.2.r \(\chi_{2900}(99, \cdot)\) n/a 532 2
2900.2.s \(\chi_{2900}(157, \cdot)\) 2900.2.s.a 2 2
2900.2.s.b 2
2900.2.s.c 16
2900.2.s.d 30
2900.2.s.e 40
2900.2.u \(\chi_{2900}(581, \cdot)\) n/a 280 4
2900.2.v \(\chi_{2900}(401, \cdot)\) n/a 282 6
2900.2.x \(\chi_{2900}(289, \cdot)\) n/a 304 4
2900.2.z \(\chi_{2900}(929, \cdot)\) n/a 280 4
2900.2.bc \(\chi_{2900}(521, \cdot)\) n/a 296 4
2900.2.bf \(\chi_{2900}(149, \cdot)\) n/a 264 6
2900.2.bh \(\chi_{2900}(701, \cdot)\) n/a 288 6
2900.2.bi \(\chi_{2900}(49, \cdot)\) n/a 276 6
2900.2.bl \(\chi_{2900}(133, \cdot)\) n/a 600 8
2900.2.bn \(\chi_{2900}(191, \cdot)\) n/a 3568 8
2900.2.bp \(\chi_{2900}(347, \cdot)\) n/a 3568 8
2900.2.bq \(\chi_{2900}(523, \cdot)\) n/a 3360 8
2900.2.bs \(\chi_{2900}(539, \cdot)\) n/a 3568 8
2900.2.bu \(\chi_{2900}(17, \cdot)\) n/a 600 8
2900.2.bw \(\chi_{2900}(193, \cdot)\) n/a 540 12
2900.2.by \(\chi_{2900}(599, \cdot)\) n/a 3192 12
2900.2.cb \(\chi_{2900}(207, \cdot)\) n/a 3192 12
2900.2.cc \(\chi_{2900}(7, \cdot)\) n/a 3192 12
2900.2.cf \(\chi_{2900}(251, \cdot)\) n/a 3348 12
2900.2.ch \(\chi_{2900}(657, \cdot)\) n/a 540 12
2900.2.ci \(\chi_{2900}(81, \cdot)\) n/a 1824 24
2900.2.cj \(\chi_{2900}(121, \cdot)\) n/a 1776 24
2900.2.cm \(\chi_{2900}(169, \cdot)\) n/a 1776 24
2900.2.co \(\chi_{2900}(9, \cdot)\) n/a 1824 24
2900.2.cq \(\chi_{2900}(73, \cdot)\) n/a 3600 48
2900.2.ct \(\chi_{2900}(19, \cdot)\) n/a 21408 48
2900.2.cv \(\chi_{2900}(23, \cdot)\) n/a 21408 48
2900.2.cw \(\chi_{2900}(63, \cdot)\) n/a 21408 48
2900.2.cy \(\chi_{2900}(11, \cdot)\) n/a 21408 48
2900.2.db \(\chi_{2900}(37, \cdot)\) n/a 3600 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2900))\)\(^{\oplus 1}\)