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Properties

Label 2700.3
Level 2700
Weight 3
Dimension 164507
Nonzero newspaces 36
Sturm bound 1166400
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1166400\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2700))\).

Total New Old
Modular forms 393000 165819 227181
Cusp forms 384600 164507 220093
Eisenstein series 8400 1312 7088

Trace form

\( 164507 q - 53 q^{2} - 93 q^{4} - 128 q^{5} - 126 q^{6} - 4 q^{7} - 29 q^{8} - 150 q^{9} + O(q^{10}) \) \( 164507 q - 53 q^{2} - 93 q^{4} - 128 q^{5} - 126 q^{6} - 4 q^{7} - 29 q^{8} - 150 q^{9} - 112 q^{10} + 24 q^{11} - 33 q^{12} - 134 q^{13} + 23 q^{14} - 137 q^{16} + 2 q^{17} - 99 q^{18} + 61 q^{19} - 210 q^{21} + 23 q^{22} + 147 q^{23} - 210 q^{24} - 160 q^{25} - 302 q^{26} - 326 q^{28} + 51 q^{29} - 96 q^{30} - 2 q^{31} - 503 q^{32} + 15 q^{33} - 449 q^{34} + 396 q^{35} - 96 q^{36} - 143 q^{37} - 359 q^{38} + 477 q^{39} - 288 q^{40} - 302 q^{41} - 198 q^{42} + 106 q^{43} - 173 q^{44} - 252 q^{45} - 75 q^{46} - 570 q^{47} - 291 q^{48} - 439 q^{49} - 424 q^{50} - 771 q^{51} - 557 q^{52} - 1384 q^{53} + 6 q^{54} - 200 q^{55} - 587 q^{56} - 987 q^{57} - 673 q^{58} - 294 q^{59} - 96 q^{60} - 646 q^{61} + 10 q^{62} + 381 q^{63} + 69 q^{64} + 304 q^{65} + 273 q^{66} + 319 q^{67} + 292 q^{68} + 381 q^{69} + 128 q^{70} - 60 q^{71} - 1380 q^{72} - 1526 q^{73} - 2569 q^{74} - 1008 q^{75} - 1681 q^{76} - 3856 q^{77} - 2754 q^{78} - 1650 q^{79} - 2664 q^{80} - 1602 q^{81} - 2094 q^{82} - 3102 q^{83} - 1590 q^{84} - 1248 q^{85} - 1187 q^{86} - 921 q^{87} - 217 q^{88} - 1965 q^{89} + 132 q^{90} - 186 q^{91} + 2401 q^{92} - 711 q^{93} + 1067 q^{94} + 912 q^{95} + 3378 q^{96} + 451 q^{97} + 5840 q^{98} + 1455 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2700))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2700.3.b \(\chi_{2700}(1349, \cdot)\) 2700.3.b.a 2 1
2700.3.b.b 2
2700.3.b.c 2
2700.3.b.d 2
2700.3.b.e 2
2700.3.b.f 2
2700.3.b.g 4
2700.3.b.h 4
2700.3.b.i 4
2700.3.b.j 4
2700.3.b.k 4
2700.3.b.l 4
2700.3.b.m 6
2700.3.b.n 6
2700.3.c \(\chi_{2700}(1351, \cdot)\) n/a 304 1
2700.3.f \(\chi_{2700}(1999, \cdot)\) n/a 288 1
2700.3.g \(\chi_{2700}(701, \cdot)\) 2700.3.g.a 1 1
2700.3.g.b 1
2700.3.g.c 1
2700.3.g.d 1
2700.3.g.e 1
2700.3.g.f 1
2700.3.g.g 1
2700.3.g.h 2
2700.3.g.i 2
2700.3.g.j 2
2700.3.g.k 2
2700.3.g.l 2
2700.3.g.m 2
2700.3.g.n 4
2700.3.g.o 4
2700.3.g.p 4
2700.3.g.q 6
2700.3.g.r 6
2700.3.g.s 8
2700.3.l \(\chi_{2700}(757, \cdot)\) 2700.3.l.a 4 2
2700.3.l.b 4
2700.3.l.c 4
2700.3.l.d 4
2700.3.l.e 4
2700.3.l.f 4
2700.3.l.g 8
2700.3.l.h 8
2700.3.l.i 8
2700.3.l.j 8
2700.3.l.k 12
2700.3.l.l 12
2700.3.l.m 16
2700.3.m \(\chi_{2700}(107, \cdot)\) n/a 576 2
2700.3.p \(\chi_{2700}(1601, \cdot)\) 2700.3.p.a 4 2
2700.3.p.b 4
2700.3.p.c 12
2700.3.p.d 16
2700.3.p.e 16
2700.3.p.f 24
2700.3.q \(\chi_{2700}(199, \cdot)\) n/a 424 2
2700.3.t \(\chi_{2700}(451, \cdot)\) n/a 444 2
2700.3.u \(\chi_{2700}(449, \cdot)\) 2700.3.u.a 8 2
2700.3.u.b 8
2700.3.u.c 24
2700.3.u.d 32
2700.3.y \(\chi_{2700}(271, \cdot)\) n/a 1920 4
2700.3.z \(\chi_{2700}(269, \cdot)\) n/a 320 4
2700.3.bb \(\chi_{2700}(161, \cdot)\) n/a 320 4
2700.3.bc \(\chi_{2700}(379, \cdot)\) n/a 1920 4
2700.3.bd \(\chi_{2700}(793, \cdot)\) n/a 144 4
2700.3.be \(\chi_{2700}(143, \cdot)\) n/a 848 4
2700.3.bi \(\chi_{2700}(149, \cdot)\) n/a 648 6
2700.3.bj \(\chi_{2700}(151, \cdot)\) n/a 4068 6
2700.3.bl \(\chi_{2700}(101, \cdot)\) n/a 684 6
2700.3.bo \(\chi_{2700}(499, \cdot)\) n/a 3864 6
2700.3.bp \(\chi_{2700}(323, \cdot)\) n/a 3840 8
2700.3.bq \(\chi_{2700}(217, \cdot)\) n/a 640 8
2700.3.bt \(\chi_{2700}(19, \cdot)\) n/a 2848 8
2700.3.bu \(\chi_{2700}(341, \cdot)\) n/a 480 8
2700.3.bw \(\chi_{2700}(89, \cdot)\) n/a 480 8
2700.3.bx \(\chi_{2700}(91, \cdot)\) n/a 2848 8
2700.3.ca \(\chi_{2700}(407, \cdot)\) n/a 7728 12
2700.3.cc \(\chi_{2700}(157, \cdot)\) n/a 1296 12
2700.3.ch \(\chi_{2700}(287, \cdot)\) n/a 5696 16
2700.3.ci \(\chi_{2700}(37, \cdot)\) n/a 960 16
2700.3.cj \(\chi_{2700}(79, \cdot)\) n/a 25824 24
2700.3.cm \(\chi_{2700}(41, \cdot)\) n/a 4320 24
2700.3.co \(\chi_{2700}(31, \cdot)\) n/a 25824 24
2700.3.cp \(\chi_{2700}(29, \cdot)\) n/a 4320 24
2700.3.cr \(\chi_{2700}(13, \cdot)\) n/a 8640 48
2700.3.ct \(\chi_{2700}(23, \cdot)\) n/a 51648 48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2700))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2700)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 2}\)