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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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