# Properties

 Label 3264.2 Level 3264 Weight 2 Dimension 122892 Nonzero newspaces 68 Sturm bound 1179648 Trace bound 65

## Defining parameters

 Level: $$N$$ = $$3264 = 2^{6} \cdot 3 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$68$$ Sturm bound: $$1179648$$ Trace bound: $$65$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3264))$$.

Total New Old
Modular forms 299520 124212 175308
Cusp forms 290305 122892 167413
Eisenstein series 9215 1320 7895

## Trace form

 $$122892 q - 84 q^{3} - 224 q^{4} - 112 q^{6} - 176 q^{7} - 140 q^{9} + O(q^{10})$$ $$122892 q - 84 q^{3} - 224 q^{4} - 112 q^{6} - 176 q^{7} - 140 q^{9} - 224 q^{10} - 16 q^{11} - 112 q^{12} - 256 q^{13} - 96 q^{15} - 224 q^{16} - 16 q^{17} - 240 q^{18} - 200 q^{19} - 104 q^{21} - 192 q^{22} - 32 q^{24} - 236 q^{25} + 160 q^{26} - 60 q^{27} - 64 q^{28} + 64 q^{29} + 48 q^{30} - 80 q^{31} + 160 q^{32} - 8 q^{33} - 160 q^{34} + 48 q^{35} + 48 q^{36} - 160 q^{37} + 160 q^{38} - 40 q^{39} - 64 q^{40} + 64 q^{41} - 32 q^{42} - 152 q^{43} + 32 q^{44} - 24 q^{45} - 224 q^{46} - 112 q^{48} - 364 q^{49} - 96 q^{50} - 24 q^{51} - 672 q^{52} - 144 q^{54} + 144 q^{55} - 224 q^{56} - 88 q^{57} - 512 q^{58} + 320 q^{59} - 304 q^{60} - 224 q^{61} - 192 q^{62} - 16 q^{63} - 608 q^{64} + 32 q^{65} - 272 q^{66} + 184 q^{67} - 96 q^{68} - 312 q^{69} - 608 q^{70} + 256 q^{71} - 112 q^{72} - 280 q^{73} - 224 q^{74} + 12 q^{75} - 480 q^{76} - 96 q^{77} - 256 q^{78} - 80 q^{79} - 96 q^{80} - 324 q^{81} - 224 q^{82} - 80 q^{83} - 336 q^{84} - 288 q^{85} - 200 q^{87} - 224 q^{88} - 64 q^{89} - 400 q^{90} - 288 q^{91} - 224 q^{93} - 224 q^{94} - 96 q^{95} - 384 q^{96} - 264 q^{97} - 200 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3264))$$

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
3264.2.a $$\chi_{3264}(1, \cdot)$$ 3264.2.a.a 1 1
3264.2.a.b 1
3264.2.a.c 1
3264.2.a.d 1
3264.2.a.e 1
3264.2.a.f 1
3264.2.a.g 1
3264.2.a.h 1
3264.2.a.i 1
3264.2.a.j 1
3264.2.a.k 1
3264.2.a.l 1
3264.2.a.m 1
3264.2.a.n 1
3264.2.a.o 1
3264.2.a.p 1
3264.2.a.q 1
3264.2.a.r 1
3264.2.a.s 1
3264.2.a.t 1
3264.2.a.u 1
3264.2.a.v 1
3264.2.a.w 1
3264.2.a.x 1
3264.2.a.y 1
3264.2.a.z 1
3264.2.a.ba 1
3264.2.a.bb 1
3264.2.a.bc 1
3264.2.a.bd 1
3264.2.a.be 1
3264.2.a.bf 1
3264.2.a.bg 2
3264.2.a.bh 2
3264.2.a.bi 2
3264.2.a.bj 2
3264.2.a.bk 2
3264.2.a.bl 2
3264.2.a.bm 2
3264.2.a.bn 2
3264.2.a.bo 2
3264.2.a.bp 2
3264.2.a.bq 3
3264.2.a.br 3
3264.2.a.bs 3
3264.2.a.bt 3
3264.2.c $$\chi_{3264}(577, \cdot)$$ 3264.2.c.a 2 1
3264.2.c.b 2
3264.2.c.c 2
3264.2.c.d 2
3264.2.c.e 2
3264.2.c.f 2
3264.2.c.g 2
3264.2.c.h 2
3264.2.c.i 2
3264.2.c.j 2
3264.2.c.k 4
3264.2.c.l 4
3264.2.c.m 4
3264.2.c.n 6
3264.2.c.o 6
3264.2.c.p 8
3264.2.c.q 10
3264.2.c.r 10
3264.2.e $$\chi_{3264}(2687, \cdot)$$ n/a 128 1
3264.2.f $$\chi_{3264}(1633, \cdot)$$ 3264.2.f.a 2 1
3264.2.f.b 2
3264.2.f.c 4
3264.2.f.d 4
3264.2.f.e 4
3264.2.f.f 8
3264.2.f.g 8
3264.2.f.h 8
3264.2.f.i 8
3264.2.f.j 16
3264.2.h $$\chi_{3264}(1631, \cdot)$$ n/a 144 1
3264.2.j $$\chi_{3264}(1055, \cdot)$$ n/a 128 1
3264.2.l $$\chi_{3264}(2209, \cdot)$$ 3264.2.l.a 4 1
3264.2.l.b 4
3264.2.l.c 8
3264.2.l.d 8
3264.2.l.e 24
3264.2.l.f 24
3264.2.o $$\chi_{3264}(3263, \cdot)$$ n/a 140 1
3264.2.r $$\chi_{3264}(47, \cdot)$$ n/a 280 2
3264.2.s $$\chi_{3264}(625, \cdot)$$ n/a 144 2
3264.2.u $$\chi_{3264}(817, \cdot)$$ n/a 128 2
3264.2.w $$\chi_{3264}(815, \cdot)$$ n/a 280 2
3264.2.y $$\chi_{3264}(863, \cdot)$$ n/a 288 2
3264.2.ba $$\chi_{3264}(1441, \cdot)$$ n/a 144 2
3264.2.bd $$\chi_{3264}(769, \cdot)$$ n/a 144 2
3264.2.bf $$\chi_{3264}(191, \cdot)$$ n/a 280 2
3264.2.bh $$\chi_{3264}(239, \cdot)$$ n/a 256 2
3264.2.bj $$\chi_{3264}(1393, \cdot)$$ n/a 144 2
3264.2.bl $$\chi_{3264}(1585, \cdot)$$ n/a 144 2
3264.2.bm $$\chi_{3264}(1007, \cdot)$$ n/a 280 2
3264.2.bp $$\chi_{3264}(1511, \cdot)$$ None 0 4
3264.2.br $$\chi_{3264}(553, \cdot)$$ None 0 4
3264.2.bt $$\chi_{3264}(455, \cdot)$$ None 0 4
3264.2.bv $$\chi_{3264}(1033, \cdot)$$ None 0 4
3264.2.bx $$\chi_{3264}(263, \cdot)$$ None 0 4
3264.2.bz $$\chi_{3264}(457, \cdot)$$ None 0 4
3264.2.cc $$\chi_{3264}(961, \cdot)$$ n/a 288 4
3264.2.cd $$\chi_{3264}(383, \cdot)$$ n/a 560 4
3264.2.ce $$\chi_{3264}(1103, \cdot)$$ n/a 560 4
3264.2.cf $$\chi_{3264}(433, \cdot)$$ n/a 288 4
3264.2.ci $$\chi_{3264}(169, \cdot)$$ None 0 4
3264.2.cj $$\chi_{3264}(647, \cdot)$$ None 0 4
3264.2.cm $$\chi_{3264}(407, \cdot)$$ None 0 4
3264.2.cn $$\chi_{3264}(409, \cdot)$$ None 0 4
3264.2.cq $$\chi_{3264}(1487, \cdot)$$ n/a 560 4
3264.2.cr $$\chi_{3264}(49, \cdot)$$ n/a 288 4
3264.2.cu $$\chi_{3264}(865, \cdot)$$ n/a 288 4
3264.2.cv $$\chi_{3264}(287, \cdot)$$ n/a 576 4
3264.2.cz $$\chi_{3264}(25, \cdot)$$ None 0 4
3264.2.db $$\chi_{3264}(1607, \cdot)$$ None 0 4
3264.2.dc $$\chi_{3264}(217, \cdot)$$ None 0 4
3264.2.de $$\chi_{3264}(1271, \cdot)$$ None 0 4
3264.2.dh $$\chi_{3264}(121, \cdot)$$ None 0 4
3264.2.dj $$\chi_{3264}(359, \cdot)$$ None 0 4
3264.2.dm $$\chi_{3264}(197, \cdot)$$ n/a 4576 8
3264.2.dn $$\chi_{3264}(403, \cdot)$$ n/a 2304 8
3264.2.do $$\chi_{3264}(229, \cdot)$$ n/a 2304 8
3264.2.dq $$\chi_{3264}(563, \cdot)$$ n/a 4576 8
3264.2.ds $$\chi_{3264}(139, \cdot)$$ n/a 2304 8
3264.2.dt $$\chi_{3264}(317, \cdot)$$ n/a 4576 8
3264.2.dx $$\chi_{3264}(113, \cdot)$$ n/a 1120 8
3264.2.dy $$\chi_{3264}(79, \cdot)$$ n/a 576 8
3264.2.eb $$\chi_{3264}(7, \cdot)$$ None 0 8
3264.2.ec $$\chi_{3264}(233, \cdot)$$ None 0 8
3264.2.ee $$\chi_{3264}(467, \cdot)$$ n/a 4576 8
3264.2.eg $$\chi_{3264}(349, \cdot)$$ n/a 2304 8
3264.2.ek $$\chi_{3264}(245, \cdot)$$ n/a 4576 8
3264.2.el $$\chi_{3264}(283, \cdot)$$ n/a 2304 8
3264.2.eo $$\chi_{3264}(29, \cdot)$$ n/a 4576 8
3264.2.ep $$\chi_{3264}(91, \cdot)$$ n/a 2304 8
3264.2.eq $$\chi_{3264}(499, \cdot)$$ n/a 2304 8
3264.2.er $$\chi_{3264}(437, \cdot)$$ n/a 4576 8
3264.2.ew $$\chi_{3264}(205, \cdot)$$ n/a 2048 8
3264.2.ex $$\chi_{3264}(203, \cdot)$$ n/a 4576 8
3264.2.ez $$\chi_{3264}(65, \cdot)$$ n/a 1120 8
3264.2.fa $$\chi_{3264}(703, \cdot)$$ n/a 576 8
3264.2.fc $$\chi_{3264}(41, \cdot)$$ None 0 8
3264.2.ff $$\chi_{3264}(199, \cdot)$$ None 0 8
3264.2.fg $$\chi_{3264}(13, \cdot)$$ n/a 2304 8
3264.2.fh $$\chi_{3264}(251, \cdot)$$ n/a 4576 8
3264.2.fm $$\chi_{3264}(157, \cdot)$$ n/a 2304 8
3264.2.fn $$\chi_{3264}(395, \cdot)$$ n/a 4576 8
3264.2.fo $$\chi_{3264}(473, \cdot)$$ None 0 8
3264.2.fr $$\chi_{3264}(1159, \cdot)$$ None 0 8
3264.2.ft $$\chi_{3264}(31, \cdot)$$ n/a 576 8
3264.2.fu $$\chi_{3264}(737, \cdot)$$ n/a 1152 8
3264.2.fw $$\chi_{3264}(35, \cdot)$$ n/a 4096 8
3264.2.fx $$\chi_{3264}(373, \cdot)$$ n/a 2304 8
3264.2.ga $$\chi_{3264}(581, \cdot)$$ n/a 4576 8
3264.2.gb $$\chi_{3264}(163, \cdot)$$ n/a 2304 8
3264.2.ge $$\chi_{3264}(325, \cdot)$$ n/a 2304 8
3264.2.gg $$\chi_{3264}(155, \cdot)$$ n/a 4576 8
3264.2.gi $$\chi_{3264}(439, \cdot)$$ None 0 8
3264.2.gl $$\chi_{3264}(1193, \cdot)$$ None 0 8
3264.2.gn $$\chi_{3264}(401, \cdot)$$ n/a 1120 8
3264.2.go $$\chi_{3264}(367, \cdot)$$ n/a 576 8
3264.2.gq $$\chi_{3264}(379, \cdot)$$ n/a 2304 8
3264.2.gr $$\chi_{3264}(5, \cdot)$$ n/a 4576 8
3264.2.gu $$\chi_{3264}(59, \cdot)$$ n/a 4576 8
3264.2.gw $$\chi_{3264}(253, \cdot)$$ n/a 2304 8
3264.2.ha $$\chi_{3264}(547, \cdot)$$ n/a 2304 8
3264.2.hb $$\chi_{3264}(533, \cdot)$$ n/a 4576 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3264))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3264)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(272))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(408))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(544))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(816))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1088))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1632))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3264))$$$$^{\oplus 1}$$