Properties

Label 2700.2
Level 2700
Weight 2
Dimension 81925
Nonzero newspaces 36
Sturm bound 777600
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(777600\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2700))\).

Total New Old
Modular forms 198600 83237 115363
Cusp forms 190201 81925 108276
Eisenstein series 8399 1312 7087

Trace form

\( 81925q - 51q^{2} - 89q^{4} - 128q^{5} - 126q^{6} + 6q^{7} - 57q^{8} - 150q^{9} + O(q^{10}) \) \( 81925q - 51q^{2} - 89q^{4} - 128q^{5} - 126q^{6} + 6q^{7} - 57q^{8} - 150q^{9} - 112q^{10} + 22q^{11} - 87q^{12} - 168q^{13} - 89q^{14} - 169q^{16} - 114q^{17} - 99q^{18} + 7q^{19} - 80q^{20} - 282q^{21} - 137q^{22} - 57q^{23} - 84q^{24} - 240q^{25} - 224q^{26} - 27q^{27} - 262q^{28} - 211q^{29} - 96q^{30} - 32q^{31} - 71q^{32} - 228q^{33} - 125q^{34} - 84q^{35} - 96q^{36} - 279q^{37} - 43q^{38} - 117q^{39} - 128q^{40} - 378q^{41} - 18q^{42} - 128q^{43} + 55q^{44} - 252q^{45} - 115q^{46} - 180q^{47} - 3q^{48} - 376q^{49} - 24q^{50} - 33q^{51} - 29q^{52} - 330q^{53} + 6q^{54} - 40q^{55} + 113q^{56} - 186q^{57} + 19q^{58} - 43q^{59} - 96q^{60} - 420q^{61} + 146q^{62} + 57q^{63} + 25q^{64} - 256q^{65} - 33q^{66} - 89q^{67} + 282q^{68} - 141q^{69} - 32q^{70} - 20q^{71} + 132q^{72} - 180q^{73} + 351q^{74} + 72q^{75} - 73q^{76} - 20q^{77} + 216q^{78} + 68q^{79} + 256q^{80} - 90q^{81} + 134q^{82} + 262q^{83} + 372q^{84} - 208q^{85} + 589q^{86} + 177q^{87} + 247q^{88} + 384q^{89} + 132q^{90} + 256q^{91} + 597q^{92} + 171q^{93} + 235q^{94} + 232q^{95} + 174q^{96} - 27q^{97} + 612q^{98} + 267q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2700))\)

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
2700.2.a \(\chi_{2700}(1, \cdot)\) 2700.2.a.a 1 1
2700.2.a.b 1
2700.2.a.c 1
2700.2.a.d 1
2700.2.a.e 1
2700.2.a.f 1
2700.2.a.g 1
2700.2.a.h 1
2700.2.a.i 1
2700.2.a.j 1
2700.2.a.k 1
2700.2.a.l 1
2700.2.a.m 1
2700.2.a.n 1
2700.2.a.o 1
2700.2.a.p 1
2700.2.a.q 1
2700.2.a.r 1
2700.2.a.s 1
2700.2.a.t 1
2700.2.a.u 1
2700.2.a.v 2
2700.2.a.w 2
2700.2.d \(\chi_{2700}(649, \cdot)\) 2700.2.d.a 2 1
2700.2.d.b 2
2700.2.d.c 2
2700.2.d.d 2
2700.2.d.e 2
2700.2.d.f 2
2700.2.d.g 2
2700.2.d.h 2
2700.2.d.i 2
2700.2.d.j 2
2700.2.d.k 2
2700.2.d.l 2
2700.2.e \(\chi_{2700}(2051, \cdot)\) n/a 152 1
2700.2.h \(\chi_{2700}(2699, \cdot)\) n/a 144 1
2700.2.i \(\chi_{2700}(901, \cdot)\) 2700.2.i.a 2 2
2700.2.i.b 2
2700.2.i.c 6
2700.2.i.d 8
2700.2.i.e 8
2700.2.i.f 12
2700.2.j \(\chi_{2700}(593, \cdot)\) 2700.2.j.a 4 2
2700.2.j.b 4
2700.2.j.c 4
2700.2.j.d 4
2700.2.j.e 4
2700.2.j.f 4
2700.2.j.g 4
2700.2.j.h 4
2700.2.j.i 8
2700.2.j.j 8
2700.2.k \(\chi_{2700}(1243, \cdot)\) n/a 288 2
2700.2.n \(\chi_{2700}(541, \cdot)\) n/a 160 4
2700.2.o \(\chi_{2700}(899, \cdot)\) n/a 208 2
2700.2.r \(\chi_{2700}(251, \cdot)\) n/a 216 2
2700.2.s \(\chi_{2700}(1549, \cdot)\) 2700.2.s.a 4 2
2700.2.s.b 4
2700.2.s.c 12
2700.2.s.d 16
2700.2.v \(\chi_{2700}(301, \cdot)\) n/a 342 6
2700.2.w \(\chi_{2700}(431, \cdot)\) n/a 960 4
2700.2.x \(\chi_{2700}(109, \cdot)\) n/a 160 4
2700.2.ba \(\chi_{2700}(539, \cdot)\) n/a 960 4
2700.2.bf \(\chi_{2700}(557, \cdot)\) 2700.2.bf.a 4 4
2700.2.bf.b 4
2700.2.bf.c 4
2700.2.bf.d 4
2700.2.bf.e 24
2700.2.bf.f 32
2700.2.bg \(\chi_{2700}(307, \cdot)\) n/a 416 4
2700.2.bh \(\chi_{2700}(181, \cdot)\) n/a 240 8
2700.2.bk \(\chi_{2700}(299, \cdot)\) n/a 1920 6
2700.2.bm \(\chi_{2700}(49, \cdot)\) n/a 324 6
2700.2.bn \(\chi_{2700}(551, \cdot)\) n/a 2016 6
2700.2.br \(\chi_{2700}(163, \cdot)\) n/a 1920 8
2700.2.bs \(\chi_{2700}(53, \cdot)\) n/a 320 8
2700.2.bv \(\chi_{2700}(179, \cdot)\) n/a 1408 8
2700.2.by \(\chi_{2700}(289, \cdot)\) n/a 240 8
2700.2.bz \(\chi_{2700}(71, \cdot)\) n/a 1408 8
2700.2.cb \(\chi_{2700}(7, \cdot)\) n/a 3840 12
2700.2.cd \(\chi_{2700}(257, \cdot)\) n/a 648 12
2700.2.ce \(\chi_{2700}(61, \cdot)\) n/a 2160 24
2700.2.cf \(\chi_{2700}(127, \cdot)\) n/a 2816 16
2700.2.cg \(\chi_{2700}(17, \cdot)\) n/a 480 16
2700.2.ck \(\chi_{2700}(11, \cdot)\) n/a 12864 24
2700.2.cl \(\chi_{2700}(169, \cdot)\) n/a 2160 24
2700.2.cn \(\chi_{2700}(59, \cdot)\) n/a 12864 24
2700.2.cq \(\chi_{2700}(77, \cdot)\) n/a 4320 48
2700.2.cs \(\chi_{2700}(67, \cdot)\) n/a 25728 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2700))\) into lower level spaces

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