# Properties

 Label 3240.2 Level 3240 Weight 2 Dimension 113376 Nonzero newspaces 36 Sturm bound 1119744 Trace bound 42

## Defining parameters

 Level: $$N$$ = $$3240 = 2^{3} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$1119744$$ Trace bound: $$42$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3240))$$.

Total New Old
Modular forms 285120 114720 170400
Cusp forms 274753 113376 161377
Eisenstein series 10367 1344 9023

## Trace form

 $$113376 q - 48 q^{2} - 72 q^{3} - 80 q^{4} - 216 q^{6} - 80 q^{7} - 48 q^{8} - 144 q^{9} + O(q^{10})$$ $$113376 q - 48 q^{2} - 72 q^{3} - 80 q^{4} - 216 q^{6} - 80 q^{7} - 48 q^{8} - 144 q^{9} - 174 q^{10} - 138 q^{11} - 72 q^{12} + 12 q^{13} - 48 q^{14} - 108 q^{15} - 240 q^{16} - 72 q^{17} - 72 q^{18} - 104 q^{19} - 72 q^{20} - 96 q^{22} - 24 q^{23} - 72 q^{24} - 234 q^{25} - 180 q^{26} - 72 q^{27} - 164 q^{28} - 36 q^{29} - 108 q^{30} - 276 q^{31} - 168 q^{32} - 144 q^{33} - 152 q^{34} - 114 q^{35} - 216 q^{36} - 36 q^{37} - 168 q^{38} - 72 q^{39} - 156 q^{40} - 366 q^{41} - 72 q^{42} - 158 q^{43} - 144 q^{44} - 54 q^{45} - 380 q^{46} - 264 q^{47} - 72 q^{48} - 244 q^{49} - 72 q^{50} - 342 q^{51} - 112 q^{52} - 180 q^{53} - 72 q^{54} - 266 q^{55} - 60 q^{56} - 252 q^{57} - 32 q^{58} - 330 q^{59} - 108 q^{60} - 120 q^{61} + 84 q^{62} - 180 q^{63} - 44 q^{64} - 270 q^{65} - 216 q^{66} - 218 q^{67} + 108 q^{68} - 36 q^{69} - 20 q^{70} - 300 q^{71} - 72 q^{72} - 280 q^{73} + 96 q^{74} - 108 q^{75} - 96 q^{76} - 120 q^{77} + 36 q^{78} - 212 q^{79} + 18 q^{80} - 432 q^{81} - 152 q^{82} - 228 q^{83} - 72 q^{84} - 72 q^{85} - 24 q^{86} - 72 q^{87} + 192 q^{88} - 96 q^{89} + 18 q^{90} - 308 q^{91} + 552 q^{92} + 108 q^{93} + 188 q^{94} + 78 q^{95} + 252 q^{96} - 70 q^{97} + 1092 q^{98} + 252 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3240))$$

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
3240.2.a $$\chi_{3240}(1, \cdot)$$ 3240.2.a.a 1 1
3240.2.a.b 1
3240.2.a.c 1
3240.2.a.d 1
3240.2.a.e 1
3240.2.a.f 1
3240.2.a.g 2
3240.2.a.h 2
3240.2.a.i 2
3240.2.a.j 2
3240.2.a.k 2
3240.2.a.l 2
3240.2.a.m 2
3240.2.a.n 2
3240.2.a.o 2
3240.2.a.p 2
3240.2.a.q 3
3240.2.a.r 3
3240.2.a.s 4
3240.2.a.t 4
3240.2.a.u 4
3240.2.a.v 4
3240.2.b $$\chi_{3240}(971, \cdot)$$ n/a 192 1
3240.2.d $$\chi_{3240}(2269, \cdot)$$ n/a 280 1
3240.2.f $$\chi_{3240}(649, \cdot)$$ 3240.2.f.a 2 1
3240.2.f.b 2
3240.2.f.c 2
3240.2.f.d 2
3240.2.f.e 2
3240.2.f.f 2
3240.2.f.g 6
3240.2.f.h 6
3240.2.f.i 16
3240.2.f.j 16
3240.2.f.k 16
3240.2.h $$\chi_{3240}(2591, \cdot)$$ None 0 1
3240.2.k $$\chi_{3240}(1621, \cdot)$$ n/a 192 1
3240.2.m $$\chi_{3240}(1619, \cdot)$$ n/a 280 1
3240.2.o $$\chi_{3240}(3239, \cdot)$$ None 0 1
3240.2.q $$\chi_{3240}(1081, \cdot)$$ 3240.2.q.a 2 2
3240.2.q.b 2
3240.2.q.c 2
3240.2.q.d 2
3240.2.q.e 2
3240.2.q.f 2
3240.2.q.g 2
3240.2.q.h 2
3240.2.q.i 2
3240.2.q.j 2
3240.2.q.k 2
3240.2.q.l 2
3240.2.q.m 2
3240.2.q.n 2
3240.2.q.o 2
3240.2.q.p 2
3240.2.q.q 2
3240.2.q.r 2
3240.2.q.s 2
3240.2.q.t 2
3240.2.q.u 2
3240.2.q.v 2
3240.2.q.w 2
3240.2.q.x 2
3240.2.q.y 4
3240.2.q.z 4
3240.2.q.ba 4
3240.2.q.bb 4
3240.2.q.bc 4
3240.2.q.bd 4
3240.2.q.be 4
3240.2.q.bf 4
3240.2.q.bg 8
3240.2.q.bh 8
3240.2.s $$\chi_{3240}(1457, \cdot)$$ n/a 144 2
3240.2.t $$\chi_{3240}(487, \cdot)$$ None 0 2
3240.2.w $$\chi_{3240}(163, \cdot)$$ n/a 560 2
3240.2.x $$\chi_{3240}(1133, \cdot)$$ n/a 560 2
3240.2.bb $$\chi_{3240}(1079, \cdot)$$ None 0 2
3240.2.bd $$\chi_{3240}(539, \cdot)$$ n/a 568 2
3240.2.bf $$\chi_{3240}(541, \cdot)$$ n/a 384 2
3240.2.bg $$\chi_{3240}(431, \cdot)$$ None 0 2
3240.2.bi $$\chi_{3240}(1729, \cdot)$$ n/a 144 2
3240.2.bk $$\chi_{3240}(109, \cdot)$$ n/a 568 2
3240.2.bm $$\chi_{3240}(2051, \cdot)$$ n/a 384 2
3240.2.bo $$\chi_{3240}(361, \cdot)$$ n/a 216 6
3240.2.bp $$\chi_{3240}(1027, \cdot)$$ n/a 1136 4
3240.2.bs $$\chi_{3240}(53, \cdot)$$ n/a 1136 4
3240.2.bt $$\chi_{3240}(377, \cdot)$$ n/a 288 4
3240.2.bw $$\chi_{3240}(703, \cdot)$$ None 0 4
3240.2.bx $$\chi_{3240}(179, \cdot)$$ n/a 1272 6
3240.2.cc $$\chi_{3240}(181, \cdot)$$ n/a 864 6
3240.2.cd $$\chi_{3240}(359, \cdot)$$ None 0 6
3240.2.cg $$\chi_{3240}(289, \cdot)$$ n/a 324 6
3240.2.ch $$\chi_{3240}(251, \cdot)$$ n/a 864 6
3240.2.ci $$\chi_{3240}(71, \cdot)$$ None 0 6
3240.2.cj $$\chi_{3240}(469, \cdot)$$ n/a 1272 6
3240.2.cm $$\chi_{3240}(121, \cdot)$$ n/a 1944 18
3240.2.cp $$\chi_{3240}(197, \cdot)$$ n/a 2544 12
3240.2.cq $$\chi_{3240}(127, \cdot)$$ None 0 12
3240.2.ct $$\chi_{3240}(17, \cdot)$$ n/a 648 12
3240.2.cu $$\chi_{3240}(307, \cdot)$$ n/a 2544 12
3240.2.cx $$\chi_{3240}(229, \cdot)$$ n/a 11592 18
3240.2.cy $$\chi_{3240}(119, \cdot)$$ None 0 18
3240.2.da $$\chi_{3240}(11, \cdot)$$ n/a 7776 18
3240.2.dc $$\chi_{3240}(191, \cdot)$$ None 0 18
3240.2.de $$\chi_{3240}(59, \cdot)$$ n/a 11592 18
3240.2.dh $$\chi_{3240}(49, \cdot)$$ n/a 2916 18
3240.2.dj $$\chi_{3240}(61, \cdot)$$ n/a 7776 18
3240.2.dk $$\chi_{3240}(77, \cdot)$$ n/a 23184 36
3240.2.dn $$\chi_{3240}(43, \cdot)$$ n/a 23184 36
3240.2.do $$\chi_{3240}(113, \cdot)$$ n/a 5832 36
3240.2.dr $$\chi_{3240}(7, \cdot)$$ None 0 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3240))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3240)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(810))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1620))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3240))$$$$^{\oplus 1}$$