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Properties

Label 2664.2
Level 2664
Weight 2
Dimension 86965
Nonzero newspaces 72
Sturm bound 787968
Trace bound 47

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Defining parameters

Level: \( N \) = \( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(787968\)
Trace bound: \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2664))\).

Total New Old
Modular forms 200448 88225 112223
Cusp forms 193537 86965 106572
Eisenstein series 6911 1260 5651

Trace form

\( 86965 q - 104 q^{2} - 138 q^{3} - 104 q^{4} - 8 q^{5} - 128 q^{6} - 104 q^{7} - 80 q^{8} - 270 q^{9} + O(q^{10}) \) \( 86965 q - 104 q^{2} - 138 q^{3} - 104 q^{4} - 8 q^{5} - 128 q^{6} - 104 q^{7} - 80 q^{8} - 270 q^{9} - 276 q^{10} - 74 q^{11} - 116 q^{12} + 4 q^{13} - 80 q^{14} - 96 q^{15} - 88 q^{16} - 176 q^{17} - 144 q^{18} - 280 q^{19} - 128 q^{20} + 24 q^{21} - 136 q^{22} - 72 q^{23} - 192 q^{24} - 200 q^{25} - 164 q^{26} - 144 q^{27} - 340 q^{28} - 12 q^{29} - 236 q^{30} - 76 q^{31} - 184 q^{32} - 274 q^{33} - 80 q^{34} - 180 q^{35} - 244 q^{36} - 6 q^{37} - 292 q^{38} - 216 q^{39} - 128 q^{40} - 206 q^{41} - 244 q^{42} - 158 q^{43} - 192 q^{44} - 4 q^{45} - 356 q^{46} - 192 q^{47} - 184 q^{48} - 112 q^{49} - 164 q^{50} - 162 q^{51} - 56 q^{52} + 28 q^{53} - 120 q^{54} - 292 q^{55} - 44 q^{56} - 230 q^{57} - 88 q^{58} - 146 q^{59} - 12 q^{60} - 29 q^{61} + 20 q^{62} - 208 q^{63} - 284 q^{64} - 229 q^{65} + 64 q^{66} - 94 q^{67} + 60 q^{68} - 44 q^{69} - 16 q^{70} - 196 q^{71} + 60 q^{72} - 672 q^{73} + 2 q^{74} - 386 q^{75} - 40 q^{76} - 96 q^{77} + 4 q^{78} - 172 q^{79} + 84 q^{80} - 310 q^{81} - 364 q^{82} - 208 q^{83} - 16 q^{84} - 97 q^{85} - 8 q^{86} - 180 q^{87} - 136 q^{88} - 305 q^{89} - 116 q^{90} - 408 q^{91} - 216 q^{92} + 20 q^{93} - 156 q^{94} - 236 q^{95} - 240 q^{96} - 318 q^{97} - 300 q^{98} - 204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2664))\)

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
2664.2.a \(\chi_{2664}(1, \cdot)\) 2664.2.a.a 1 1
2664.2.a.b 1
2664.2.a.c 1
2664.2.a.d 1
2664.2.a.e 1
2664.2.a.f 1
2664.2.a.g 1
2664.2.a.h 1
2664.2.a.i 2
2664.2.a.j 2
2664.2.a.k 2
2664.2.a.l 2
2664.2.a.m 3
2664.2.a.n 3
2664.2.a.o 3
2664.2.a.p 3
2664.2.a.q 3
2664.2.a.r 4
2664.2.a.s 5
2664.2.a.t 5
2664.2.c \(\chi_{2664}(1331, \cdot)\) n/a 152 1
2664.2.e \(\chi_{2664}(2591, \cdot)\) None 0 1
2664.2.f \(\chi_{2664}(1333, \cdot)\) n/a 180 1
2664.2.h \(\chi_{2664}(73, \cdot)\) 2664.2.h.a 2 1
2664.2.h.b 6
2664.2.h.c 10
2664.2.h.d 10
2664.2.h.e 20
2664.2.j \(\chi_{2664}(1259, \cdot)\) n/a 144 1
2664.2.l \(\chi_{2664}(2663, \cdot)\) None 0 1
2664.2.o \(\chi_{2664}(1405, \cdot)\) n/a 188 1
2664.2.q \(\chi_{2664}(889, \cdot)\) n/a 216 2
2664.2.r \(\chi_{2664}(433, \cdot)\) 2664.2.r.a 2 2
2664.2.r.b 2
2664.2.r.c 2
2664.2.r.d 2
2664.2.r.e 2
2664.2.r.f 2
2664.2.r.g 2
2664.2.r.h 6
2664.2.r.i 6
2664.2.r.j 6
2664.2.r.k 6
2664.2.r.l 6
2664.2.r.m 8
2664.2.r.n 10
2664.2.r.o 16
2664.2.r.p 16
2664.2.s \(\chi_{2664}(1897, \cdot)\) n/a 228 2
2664.2.t \(\chi_{2664}(121, \cdot)\) n/a 228 2
2664.2.u \(\chi_{2664}(1819, \cdot)\) n/a 376 2
2664.2.w \(\chi_{2664}(487, \cdot)\) None 0 2
2664.2.z \(\chi_{2664}(413, \cdot)\) n/a 304 2
2664.2.bb \(\chi_{2664}(1745, \cdot)\) 2664.2.bb.a 36 2
2664.2.bb.b 40
2664.2.bc \(\chi_{2664}(529, \cdot)\) n/a 228 2
2664.2.be \(\chi_{2664}(1453, \cdot)\) n/a 904 2
2664.2.bh \(\chi_{2664}(1823, \cdot)\) None 0 2
2664.2.bj \(\chi_{2664}(11, \cdot)\) n/a 904 2
2664.2.bl \(\chi_{2664}(455, \cdot)\) None 0 2
2664.2.bn \(\chi_{2664}(1379, \cdot)\) n/a 904 2
2664.2.bo \(\chi_{2664}(397, \cdot)\) n/a 376 2
2664.2.br \(\chi_{2664}(517, \cdot)\) n/a 904 2
2664.2.bv \(\chi_{2664}(1691, \cdot)\) n/a 304 2
2664.2.bx \(\chi_{2664}(887, \cdot)\) None 0 2
2664.2.bz \(\chi_{2664}(371, \cdot)\) n/a 864 2
2664.2.cb \(\chi_{2664}(1655, \cdot)\) None 0 2
2664.2.cd \(\chi_{2664}(85, \cdot)\) n/a 904 2
2664.2.cf \(\chi_{2664}(47, \cdot)\) None 0 2
2664.2.ch \(\chi_{2664}(1787, \cdot)\) n/a 904 2
2664.2.ck \(\chi_{2664}(1765, \cdot)\) n/a 376 2
2664.2.cm \(\chi_{2664}(961, \cdot)\) n/a 228 2
2664.2.co \(\chi_{2664}(445, \cdot)\) n/a 864 2
2664.2.cq \(\chi_{2664}(1729, \cdot)\) 2664.2.cq.a 8 2
2664.2.cq.b 8
2664.2.cq.c 20
2664.2.cq.d 20
2664.2.cq.e 40
2664.2.cr \(\chi_{2664}(323, \cdot)\) n/a 304 2
2664.2.ct \(\chi_{2664}(815, \cdot)\) None 0 2
2664.2.cv \(\chi_{2664}(443, \cdot)\) n/a 904 2
2664.2.cx \(\chi_{2664}(359, \cdot)\) None 0 2
2664.2.da \(\chi_{2664}(1417, \cdot)\) n/a 228 2
2664.2.dc \(\chi_{2664}(565, \cdot)\) n/a 904 2
2664.2.df \(\chi_{2664}(1861, \cdot)\) n/a 904 2
2664.2.dg \(\chi_{2664}(1343, \cdot)\) None 0 2
2664.2.di \(\chi_{2664}(491, \cdot)\) n/a 904 2
2664.2.dk \(\chi_{2664}(49, \cdot)\) n/a 684 6
2664.2.dl \(\chi_{2664}(145, \cdot)\) n/a 282 6
2664.2.dm \(\chi_{2664}(601, \cdot)\) n/a 684 6
2664.2.do \(\chi_{2664}(103, \cdot)\) None 0 4
2664.2.dq \(\chi_{2664}(763, \cdot)\) n/a 1808 4
2664.2.dr \(\chi_{2664}(125, \cdot)\) n/a 608 4
2664.2.du \(\chi_{2664}(689, \cdot)\) n/a 456 4
2664.2.dv \(\chi_{2664}(401, \cdot)\) n/a 456 4
2664.2.dy \(\chi_{2664}(29, \cdot)\) n/a 1808 4
2664.2.dz \(\chi_{2664}(1301, \cdot)\) n/a 1808 4
2664.2.eb \(\chi_{2664}(1457, \cdot)\) n/a 152 4
2664.2.ee \(\chi_{2664}(1531, \cdot)\) n/a 752 4
2664.2.ef \(\chi_{2664}(319, \cdot)\) None 0 4
2664.2.ei \(\chi_{2664}(31, \cdot)\) None 0 4
2664.2.ej \(\chi_{2664}(547, \cdot)\) n/a 1808 4
2664.2.em \(\chi_{2664}(43, \cdot)\) n/a 1808 4
2664.2.eo \(\chi_{2664}(199, \cdot)\) None 0 4
2664.2.ep \(\chi_{2664}(473, \cdot)\) n/a 456 4
2664.2.er \(\chi_{2664}(245, \cdot)\) n/a 1808 4
2664.2.eu \(\chi_{2664}(707, \cdot)\) n/a 2712 6
2664.2.ev \(\chi_{2664}(373, \cdot)\) n/a 2712 6
2664.2.ey \(\chi_{2664}(229, \cdot)\) n/a 2712 6
2664.2.ez \(\chi_{2664}(83, \cdot)\) n/a 2712 6
2664.2.fd \(\chi_{2664}(71, \cdot)\) None 0 6
2664.2.fg \(\chi_{2664}(527, \cdot)\) None 0 6
2664.2.fh \(\chi_{2664}(95, \cdot)\) None 0 6
2664.2.fk \(\chi_{2664}(215, \cdot)\) None 0 6
2664.2.fl \(\chi_{2664}(289, \cdot)\) n/a 288 6
2664.2.fo \(\chi_{2664}(817, \cdot)\) n/a 684 6
2664.2.fq \(\chi_{2664}(107, \cdot)\) n/a 912 6
2664.2.fr \(\chi_{2664}(155, \cdot)\) n/a 2712 6
2664.2.fu \(\chi_{2664}(157, \cdot)\) n/a 2712 6
2664.2.fv \(\chi_{2664}(181, \cdot)\) n/a 1128 6
2664.2.fy \(\chi_{2664}(469, \cdot)\) n/a 1128 6
2664.2.fz \(\chi_{2664}(781, \cdot)\) n/a 2712 6
2664.2.gc \(\chi_{2664}(299, \cdot)\) n/a 2712 6
2664.2.gd \(\chi_{2664}(395, \cdot)\) n/a 912 6
2664.2.gg \(\chi_{2664}(25, \cdot)\) n/a 684 6
2664.2.gh \(\chi_{2664}(743, \cdot)\) None 0 6
2664.2.gk \(\chi_{2664}(599, \cdot)\) None 0 6
2664.2.go \(\chi_{2664}(187, \cdot)\) n/a 5424 12
2664.2.gp \(\chi_{2664}(5, \cdot)\) n/a 5424 12
2664.2.gq \(\chi_{2664}(79, \cdot)\) None 0 12
2664.2.gr \(\chi_{2664}(113, \cdot)\) n/a 1368 12
2664.2.gu \(\chi_{2664}(17, \cdot)\) n/a 456 12
2664.2.gv \(\chi_{2664}(55, \cdot)\) None 0 12
2664.2.gy \(\chi_{2664}(389, \cdot)\) n/a 5424 12
2664.2.gz \(\chi_{2664}(355, \cdot)\) n/a 5424 12
2664.2.hc \(\chi_{2664}(19, \cdot)\) n/a 2256 12
2664.2.hd \(\chi_{2664}(557, \cdot)\) n/a 1824 12
2664.2.hi \(\chi_{2664}(281, \cdot)\) n/a 1368 12
2664.2.hj \(\chi_{2664}(463, \cdot)\) None 0 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2664)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2664))\)\(^{\oplus 1}\)