# Properties

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

## 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

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

## 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

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