Properties

Label 1800.3
Level 1800
Weight 3
Dimension 70553
Nonzero newspaces 36
Sturm bound 518400
Trace bound 16

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(518400\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1800))\).

Total New Old
Modular forms 175488 71291 104197
Cusp forms 170112 70553 99559
Eisenstein series 5376 738 4638

Trace form

\( 70553 q - 40 q^{2} - 54 q^{3} - 34 q^{4} - 4 q^{5} - 76 q^{6} - 30 q^{7} - 10 q^{8} - 90 q^{9} + O(q^{10}) \) \( 70553 q - 40 q^{2} - 54 q^{3} - 34 q^{4} - 4 q^{5} - 76 q^{6} - 30 q^{7} - 10 q^{8} - 90 q^{9} - 144 q^{10} - 10 q^{11} - 62 q^{12} + 60 q^{13} + 6 q^{14} - 64 q^{15} - 86 q^{16} - 46 q^{17} - 144 q^{18} - 98 q^{19} - 68 q^{20} + 92 q^{21} - 194 q^{22} + 78 q^{23} - 72 q^{24} - 18 q^{25} - 320 q^{26} - 132 q^{27} - 284 q^{28} - 108 q^{29} - 64 q^{30} - 14 q^{31} - 230 q^{32} - 310 q^{33} - 254 q^{34} - 168 q^{35} - 78 q^{36} - 228 q^{37} - 298 q^{38} - 362 q^{39} - 8 q^{40} - 284 q^{41} + 2 q^{42} - 298 q^{43} - 10 q^{44} - 396 q^{46} - 918 q^{47} - 948 q^{48} - 879 q^{49} - 908 q^{50} - 718 q^{51} - 926 q^{52} - 624 q^{53} - 800 q^{54} - 780 q^{55} - 444 q^{56} - 578 q^{57} - 30 q^{58} - 522 q^{59} + 56 q^{60} - 268 q^{61} + 1224 q^{62} + 38 q^{63} + 536 q^{64} + 378 q^{65} + 1660 q^{66} + 382 q^{67} + 2136 q^{68} + 376 q^{69} + 948 q^{70} + 1188 q^{71} + 1954 q^{72} + 1178 q^{73} + 2050 q^{74} - 352 q^{75} + 686 q^{76} - 408 q^{77} + 146 q^{78} + 510 q^{79} + 292 q^{80} - 786 q^{81} - 644 q^{82} - 688 q^{83} - 744 q^{84} - 628 q^{85} - 922 q^{86} - 374 q^{87} - 1454 q^{88} - 1072 q^{89} - 64 q^{90} - 576 q^{91} - 654 q^{92} + 416 q^{93} - 984 q^{94} - 100 q^{95} - 968 q^{96} - 1704 q^{97} + 350 q^{98} - 254 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1800))\)

We only show spaces with odd 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
1800.3.c \(\chi_{1800}(449, \cdot)\) 1800.3.c.a 4 1
1800.3.c.b 8
1800.3.c.c 8
1800.3.c.d 8
1800.3.c.e 8
1800.3.e \(\chi_{1800}(1351, \cdot)\) None 0 1
1800.3.g \(\chi_{1800}(451, \cdot)\) n/a 187 1
1800.3.i \(\chi_{1800}(1349, \cdot)\) n/a 144 1
1800.3.j \(\chi_{1800}(199, \cdot)\) None 0 1
1800.3.l \(\chi_{1800}(1601, \cdot)\) 1800.3.l.a 2 1
1800.3.l.b 4
1800.3.l.c 4
1800.3.l.d 4
1800.3.l.e 4
1800.3.l.f 4
1800.3.l.g 4
1800.3.l.h 6
1800.3.l.i 6
1800.3.n \(\chi_{1800}(701, \cdot)\) n/a 152 1
1800.3.p \(\chi_{1800}(1099, \cdot)\) n/a 178 1
1800.3.r \(\chi_{1800}(107, \cdot)\) n/a 288 2
1800.3.u \(\chi_{1800}(757, \cdot)\) n/a 356 2
1800.3.v \(\chi_{1800}(793, \cdot)\) 1800.3.v.a 2 2
1800.3.v.b 2
1800.3.v.c 2
1800.3.v.d 2
1800.3.v.e 2
1800.3.v.f 2
1800.3.v.g 2
1800.3.v.h 4
1800.3.v.i 4
1800.3.v.j 4
1800.3.v.k 4
1800.3.v.l 4
1800.3.v.m 4
1800.3.v.n 4
1800.3.v.o 4
1800.3.v.p 4
1800.3.v.q 4
1800.3.v.r 6
1800.3.v.s 6
1800.3.v.t 8
1800.3.v.u 8
1800.3.v.v 8
1800.3.y \(\chi_{1800}(143, \cdot)\) None 0 2
1800.3.ba \(\chi_{1800}(499, \cdot)\) n/a 856 2
1800.3.bb \(\chi_{1800}(101, \cdot)\) n/a 900 2
1800.3.bd \(\chi_{1800}(401, \cdot)\) n/a 228 2
1800.3.bf \(\chi_{1800}(799, \cdot)\) None 0 2
1800.3.bi \(\chi_{1800}(149, \cdot)\) n/a 856 2
1800.3.bk \(\chi_{1800}(1051, \cdot)\) n/a 900 2
1800.3.bm \(\chi_{1800}(151, \cdot)\) None 0 2
1800.3.bo \(\chi_{1800}(1049, \cdot)\) n/a 216 2
1800.3.bp \(\chi_{1800}(269, \cdot)\) n/a 960 4
1800.3.br \(\chi_{1800}(91, \cdot)\) n/a 1192 4
1800.3.bt \(\chi_{1800}(271, \cdot)\) None 0 4
1800.3.bv \(\chi_{1800}(89, \cdot)\) n/a 240 4
1800.3.bx \(\chi_{1800}(19, \cdot)\) n/a 1192 4
1800.3.bz \(\chi_{1800}(341, \cdot)\) n/a 960 4
1800.3.cb \(\chi_{1800}(161, \cdot)\) n/a 240 4
1800.3.cd \(\chi_{1800}(559, \cdot)\) None 0 4
1800.3.cf \(\chi_{1800}(193, \cdot)\) n/a 432 4
1800.3.cg \(\chi_{1800}(407, \cdot)\) None 0 4
1800.3.cj \(\chi_{1800}(443, \cdot)\) n/a 1712 4
1800.3.ck \(\chi_{1800}(157, \cdot)\) n/a 1712 4
1800.3.cn \(\chi_{1800}(287, \cdot)\) None 0 8
1800.3.cq \(\chi_{1800}(73, \cdot)\) n/a 600 8
1800.3.cr \(\chi_{1800}(37, \cdot)\) n/a 2384 8
1800.3.cu \(\chi_{1800}(323, \cdot)\) n/a 1920 8
1800.3.cw \(\chi_{1800}(79, \cdot)\) None 0 8
1800.3.cy \(\chi_{1800}(41, \cdot)\) n/a 1440 8
1800.3.da \(\chi_{1800}(221, \cdot)\) n/a 5728 8
1800.3.db \(\chi_{1800}(139, \cdot)\) n/a 5728 8
1800.3.dc \(\chi_{1800}(209, \cdot)\) n/a 1440 8
1800.3.de \(\chi_{1800}(31, \cdot)\) None 0 8
1800.3.dg \(\chi_{1800}(211, \cdot)\) n/a 5728 8
1800.3.di \(\chi_{1800}(29, \cdot)\) n/a 5728 8
1800.3.dl \(\chi_{1800}(13, \cdot)\) n/a 11456 16
1800.3.dm \(\chi_{1800}(83, \cdot)\) n/a 11456 16
1800.3.dp \(\chi_{1800}(23, \cdot)\) None 0 16
1800.3.dq \(\chi_{1800}(97, \cdot)\) n/a 2880 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1800))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1800)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)