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Properties

Label 3300.2
Level 3300
Weight 2
Dimension 113458
Nonzero newspaces 84
Sturm bound 1152000
Trace bound 22

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Defining parameters

Level: \( N \) = \( 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1152000\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3300))\).

Total New Old
Modular forms 293600 114930 178670
Cusp forms 282401 113458 168943
Eisenstein series 11199 1472 9727

Trace form

\( 113458 q + 8 q^{3} - 122 q^{4} + 4 q^{5} - 101 q^{6} - 6 q^{7} - 48 q^{8} - 120 q^{9} + O(q^{10}) \) \( 113458 q + 8 q^{3} - 122 q^{4} + 4 q^{5} - 101 q^{6} - 6 q^{7} - 48 q^{8} - 120 q^{9} - 160 q^{10} - 6 q^{11} - 126 q^{12} - 266 q^{13} - 10 q^{14} - 28 q^{15} - 178 q^{16} - 130 q^{17} + 9 q^{18} - 110 q^{19} + 40 q^{20} - 256 q^{21} - 154 q^{22} - 100 q^{23} + 41 q^{24} - 388 q^{25} + 14 q^{26} + 41 q^{27} - 44 q^{28} - 52 q^{29} + 12 q^{30} - 4 q^{31} + 80 q^{32} - 146 q^{33} - 84 q^{34} - 8 q^{35} + 35 q^{36} - 240 q^{37} + 234 q^{38} + 45 q^{39} + 112 q^{40} + 4 q^{41} + 252 q^{42} - 48 q^{43} + 210 q^{44} - 124 q^{45} + 56 q^{46} - 70 q^{47} + 190 q^{48} - 402 q^{49} + 328 q^{50} - 83 q^{51} + 160 q^{52} - 94 q^{53} + 106 q^{54} - 88 q^{55} + 24 q^{56} + 35 q^{57} - 24 q^{58} - 82 q^{59} + 12 q^{60} - 610 q^{61} - 24 q^{62} + 197 q^{63} - 194 q^{64} - 60 q^{65} - 102 q^{66} - 206 q^{67} - 64 q^{68} + 143 q^{69} - 136 q^{70} + 40 q^{71} + 88 q^{72} + 62 q^{73} + 50 q^{74} + 164 q^{75} - 228 q^{76} + 146 q^{77} + 124 q^{78} + 126 q^{79} + 8 q^{80} + 96 q^{81} + 74 q^{82} + 110 q^{83} + 254 q^{84} + 172 q^{85} + 96 q^{86} + 260 q^{87} + 18 q^{88} + 660 q^{89} + 120 q^{90} + 366 q^{91} + 254 q^{92} + 486 q^{93} + 296 q^{94} + 320 q^{95} + 512 q^{96} + 992 q^{97} + 416 q^{98} + 326 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3300))\)

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
3300.2.a \(\chi_{3300}(1, \cdot)\) 3300.2.a.a 1 1
3300.2.a.b 1
3300.2.a.c 1
3300.2.a.d 1
3300.2.a.e 1
3300.2.a.f 1
3300.2.a.g 1
3300.2.a.h 1
3300.2.a.i 1
3300.2.a.j 1
3300.2.a.k 1
3300.2.a.l 1
3300.2.a.m 1
3300.2.a.n 1
3300.2.a.o 1
3300.2.a.p 1
3300.2.a.q 1
3300.2.a.r 1
3300.2.a.s 2
3300.2.a.t 2
3300.2.a.u 2
3300.2.a.v 2
3300.2.a.w 2
3300.2.a.x 2
3300.2.c \(\chi_{3300}(1849, \cdot)\) 3300.2.c.a 2 1
3300.2.c.b 2
3300.2.c.c 2
3300.2.c.d 2
3300.2.c.e 2
3300.2.c.f 2
3300.2.c.g 2
3300.2.c.h 2
3300.2.c.i 2
3300.2.c.j 2
3300.2.c.k 4
3300.2.c.l 4
3300.2.c.m 4
3300.2.d \(\chi_{3300}(3101, \cdot)\) 3300.2.d.a 4 1
3300.2.d.b 8
3300.2.d.c 16
3300.2.d.d 16
3300.2.d.e 16
3300.2.d.f 16
3300.2.f \(\chi_{3300}(551, \cdot)\) n/a 380 1
3300.2.i \(\chi_{3300}(1099, \cdot)\) n/a 216 1
3300.2.k \(\chi_{3300}(2551, \cdot)\) n/a 228 1
3300.2.l \(\chi_{3300}(2399, \cdot)\) n/a 360 1
3300.2.n \(\chi_{3300}(1649, \cdot)\) 3300.2.n.a 8 1
3300.2.n.b 16
3300.2.n.c 16
3300.2.n.d 32
3300.2.q \(\chi_{3300}(2243, \cdot)\) n/a 848 2
3300.2.t \(\chi_{3300}(2993, \cdot)\) n/a 120 2
3300.2.u \(\chi_{3300}(2443, \cdot)\) n/a 360 2
3300.2.x \(\chi_{3300}(1693, \cdot)\) 3300.2.x.a 8 2
3300.2.x.b 8
3300.2.x.c 24
3300.2.x.d 32
3300.2.y \(\chi_{3300}(361, \cdot)\) n/a 240 4
3300.2.z \(\chi_{3300}(301, \cdot)\) n/a 152 4
3300.2.ba \(\chi_{3300}(961, \cdot)\) n/a 240 4
3300.2.bb \(\chi_{3300}(421, \cdot)\) n/a 240 4
3300.2.bc \(\chi_{3300}(181, \cdot)\) n/a 240 4
3300.2.bd \(\chi_{3300}(661, \cdot)\) n/a 208 4
3300.2.be \(\chi_{3300}(439, \cdot)\) n/a 1440 4
3300.2.bh \(\chi_{3300}(1211, \cdot)\) n/a 2400 4
3300.2.bj \(\chi_{3300}(461, \cdot)\) n/a 480 4
3300.2.bk \(\chi_{3300}(529, \cdot)\) n/a 192 4
3300.2.bn \(\chi_{3300}(59, \cdot)\) n/a 2848 4
3300.2.bo \(\chi_{3300}(811, \cdot)\) n/a 1440 4
3300.2.br \(\chi_{3300}(1229, \cdot)\) n/a 480 4
3300.2.bv \(\chi_{3300}(689, \cdot)\) n/a 480 4
3300.2.by \(\chi_{3300}(29, \cdot)\) n/a 480 4
3300.2.bz \(\chi_{3300}(149, \cdot)\) n/a 288 4
3300.2.cc \(\chi_{3300}(931, \cdot)\) n/a 1440 4
3300.2.ce \(\chi_{3300}(119, \cdot)\) n/a 2848 4
3300.2.ch \(\chi_{3300}(599, \cdot)\) n/a 1696 4
3300.2.ci \(\chi_{3300}(1259, \cdot)\) n/a 2848 4
3300.2.cl \(\chi_{3300}(151, \cdot)\) n/a 912 4
3300.2.cm \(\chi_{3300}(211, \cdot)\) n/a 1440 4
3300.2.cp \(\chi_{3300}(1531, \cdot)\) n/a 1440 4
3300.2.cr \(\chi_{3300}(179, \cdot)\) n/a 2848 4
3300.2.cu \(\chi_{3300}(629, \cdot)\) n/a 480 4
3300.2.cw \(\chi_{3300}(281, \cdot)\) n/a 480 4
3300.2.cx \(\chi_{3300}(229, \cdot)\) n/a 240 4
3300.2.da \(\chi_{3300}(971, \cdot)\) n/a 2848 4
3300.2.dc \(\chi_{3300}(19, \cdot)\) n/a 1440 4
3300.2.dd \(\chi_{3300}(799, \cdot)\) n/a 864 4
3300.2.dg \(\chi_{3300}(139, \cdot)\) n/a 1440 4
3300.2.dh \(\chi_{3300}(71, \cdot)\) n/a 2848 4
3300.2.dk \(\chi_{3300}(911, \cdot)\) n/a 2848 4
3300.2.dl \(\chi_{3300}(251, \cdot)\) n/a 1776 4
3300.2.dn \(\chi_{3300}(679, \cdot)\) n/a 1440 4
3300.2.dp \(\chi_{3300}(169, \cdot)\) n/a 240 4
3300.2.dr \(\chi_{3300}(41, \cdot)\) n/a 480 4
3300.2.du \(\chi_{3300}(101, \cdot)\) n/a 304 4
3300.2.dv \(\chi_{3300}(761, \cdot)\) n/a 480 4
3300.2.dy \(\chi_{3300}(49, \cdot)\) n/a 144 4
3300.2.dz \(\chi_{3300}(709, \cdot)\) n/a 240 4
3300.2.ec \(\chi_{3300}(1489, \cdot)\) n/a 240 4
3300.2.ee \(\chi_{3300}(1481, \cdot)\) n/a 480 4
3300.2.ef \(\chi_{3300}(79, \cdot)\) n/a 1440 4
3300.2.ei \(\chi_{3300}(191, \cdot)\) n/a 2848 4
3300.2.el \(\chi_{3300}(329, \cdot)\) n/a 480 4
3300.2.en \(\chi_{3300}(419, \cdot)\) n/a 2400 4
3300.2.eo \(\chi_{3300}(571, \cdot)\) n/a 1440 4
3300.2.er \(\chi_{3300}(167, \cdot)\) n/a 5696 8
3300.2.es \(\chi_{3300}(113, \cdot)\) n/a 960 8
3300.2.ev \(\chi_{3300}(373, \cdot)\) n/a 480 8
3300.2.ew \(\chi_{3300}(13, \cdot)\) n/a 480 8
3300.2.ex \(\chi_{3300}(337, \cdot)\) n/a 480 8
3300.2.ey \(\chi_{3300}(193, \cdot)\) n/a 288 8
3300.2.fd \(\chi_{3300}(217, \cdot)\) n/a 480 8
3300.2.fe \(\chi_{3300}(103, \cdot)\) n/a 2880 8
3300.2.fj \(\chi_{3300}(67, \cdot)\) n/a 2400 8
3300.2.fk \(\chi_{3300}(643, \cdot)\) n/a 1728 8
3300.2.fl \(\chi_{3300}(223, \cdot)\) n/a 2880 8
3300.2.fm \(\chi_{3300}(163, \cdot)\) n/a 2880 8
3300.2.fp \(\chi_{3300}(353, \cdot)\) n/a 800 8
3300.2.fq \(\chi_{3300}(257, \cdot)\) n/a 576 8
3300.2.fr \(\chi_{3300}(53, \cdot)\) n/a 960 8
3300.2.fs \(\chi_{3300}(713, \cdot)\) n/a 960 8
3300.2.fx \(\chi_{3300}(137, \cdot)\) n/a 960 8
3300.2.fy \(\chi_{3300}(767, \cdot)\) n/a 5696 8
3300.2.gd \(\chi_{3300}(263, \cdot)\) n/a 5696 8
3300.2.ge \(\chi_{3300}(503, \cdot)\) n/a 5696 8
3300.2.gf \(\chi_{3300}(83, \cdot)\) n/a 5696 8
3300.2.gg \(\chi_{3300}(107, \cdot)\) n/a 3392 8
3300.2.gj \(\chi_{3300}(247, \cdot)\) n/a 2880 8
3300.2.gk \(\chi_{3300}(73, \cdot)\) n/a 480 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1650))\)\(^{\oplus 2}\)