Properties

Label 3330.2
Level 3330
Weight 2
Dimension 71372
Nonzero newspaces 80
Sturm bound 1181952
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(1181952\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3330))\).

Total New Old
Modular forms 300096 71372 228724
Cusp forms 290881 71372 219509
Eisenstein series 9215 0 9215

Trace form

\( 71372q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + O(q^{10}) \) \( 71372q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + 22q^{10} + 52q^{11} + 16q^{12} + 28q^{13} + 40q^{14} + 48q^{15} - 6q^{16} + 36q^{17} + 8q^{18} + 16q^{19} + 22q^{20} + 72q^{21} + 20q^{22} + 72q^{23} - 12q^{24} + 34q^{25} - 30q^{26} + 48q^{27} - 24q^{28} - 60q^{29} - 200q^{31} - 6q^{32} - 20q^{33} - 152q^{34} - 140q^{35} - 20q^{36} - 142q^{37} - 156q^{38} - 128q^{39} - 39q^{40} - 368q^{41} - 128q^{42} - 164q^{43} - 64q^{44} - 160q^{45} - 144q^{46} - 192q^{47} - 20q^{48} - 102q^{49} - 103q^{50} - 60q^{51} - 20q^{52} - 60q^{53} - 60q^{54} + 40q^{55} - 40q^{56} - 52q^{57} - 68q^{58} - 92q^{59} + 16q^{60} - 118q^{61} + 80q^{63} + 6q^{64} + 3q^{65} + 96q^{66} - 36q^{67} + 72q^{68} + 128q^{69} + 48q^{70} + 12q^{72} - 28q^{73} + 50q^{74} - 12q^{75} + 92q^{76} - 120q^{77} + 56q^{78} - 80q^{79} - 10q^{80} - 4q^{81} + 116q^{82} - 144q^{83} + 24q^{84} - 21q^{85} + 140q^{86} + 40q^{87} + 20q^{88} + 2q^{89} + 112q^{90} + 128q^{91} + 288q^{92} + 368q^{93} + 488q^{94} + 408q^{95} + 16q^{96} + 952q^{97} + 918q^{98} + 760q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3330))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3330.2.a \(\chi_{3330}(1, \cdot)\) 3330.2.a.a 1 1
3330.2.a.b 1
3330.2.a.c 1
3330.2.a.d 1
3330.2.a.e 1
3330.2.a.f 1
3330.2.a.g 1
3330.2.a.h 1
3330.2.a.i 1
3330.2.a.j 1
3330.2.a.k 1
3330.2.a.l 1
3330.2.a.m 1
3330.2.a.n 1
3330.2.a.o 1
3330.2.a.p 1
3330.2.a.q 1
3330.2.a.r 1
3330.2.a.s 1
3330.2.a.t 1
3330.2.a.u 1
3330.2.a.v 1
3330.2.a.w 1
3330.2.a.x 1
3330.2.a.y 1
3330.2.a.z 1
3330.2.a.ba 1
3330.2.a.bb 2
3330.2.a.bc 2
3330.2.a.bd 2
3330.2.a.be 2
3330.2.a.bf 2
3330.2.a.bg 3
3330.2.a.bh 3
3330.2.a.bi 3
3330.2.a.bj 4
3330.2.a.bk 5
3330.2.a.bl 5
3330.2.d \(\chi_{3330}(1999, \cdot)\) 3330.2.d.a 2 1
3330.2.d.b 2
3330.2.d.c 2
3330.2.d.d 2
3330.2.d.e 2
3330.2.d.f 2
3330.2.d.g 2
3330.2.d.h 4
3330.2.d.i 4
3330.2.d.j 4
3330.2.d.k 4
3330.2.d.l 4
3330.2.d.m 4
3330.2.d.n 6
3330.2.d.o 8
3330.2.d.p 10
3330.2.d.q 14
3330.2.d.r 14
3330.2.e \(\chi_{3330}(739, \cdot)\) 3330.2.e.a 2 1
3330.2.e.b 2
3330.2.e.c 10
3330.2.e.d 10
3330.2.e.e 16
3330.2.e.f 16
3330.2.e.g 20
3330.2.e.h 20
3330.2.h \(\chi_{3330}(2071, \cdot)\) 3330.2.h.a 2 1
3330.2.h.b 2
3330.2.h.c 2
3330.2.h.d 2
3330.2.h.e 2
3330.2.h.f 2
3330.2.h.g 2
3330.2.h.h 2
3330.2.h.i 2
3330.2.h.j 4
3330.2.h.k 4
3330.2.h.l 4
3330.2.h.m 6
3330.2.h.n 6
3330.2.h.o 8
3330.2.h.p 16
3330.2.i \(\chi_{3330}(1111, \cdot)\) n/a 288 2
3330.2.j \(\chi_{3330}(121, \cdot)\) n/a 304 2
3330.2.k \(\chi_{3330}(2341, \cdot)\) n/a 132 2
3330.2.l \(\chi_{3330}(211, \cdot)\) n/a 304 2
3330.2.n \(\chi_{3330}(179, \cdot)\) n/a 152 2
3330.2.o \(\chi_{3330}(1153, \cdot)\) n/a 190 2
3330.2.p \(\chi_{3330}(593, \cdot)\) n/a 144 2
3330.2.q \(\chi_{3330}(1997, \cdot)\) n/a 152 2
3330.2.r \(\chi_{3330}(253, \cdot)\) n/a 190 2
3330.2.x \(\chi_{3330}(1511, \cdot)\) n/a 112 2
3330.2.y \(\chi_{3330}(619, \cdot)\) n/a 456 2
3330.2.z \(\chi_{3330}(2209, \cdot)\) n/a 456 2
3330.2.be \(\chi_{3330}(841, \cdot)\) n/a 304 2
3330.2.bf \(\chi_{3330}(961, \cdot)\) n/a 304 2
3330.2.bk \(\chi_{3330}(2971, \cdot)\) n/a 132 2
3330.2.bn \(\chi_{3330}(2119, \cdot)\) n/a 456 2
3330.2.bo \(\chi_{3330}(1849, \cdot)\) n/a 456 2
3330.2.bp \(\chi_{3330}(889, \cdot)\) n/a 432 2
3330.2.bq \(\chi_{3330}(529, \cdot)\) n/a 456 2
3330.2.bv \(\chi_{3330}(1639, \cdot)\) n/a 192 2
3330.2.bw \(\chi_{3330}(1009, \cdot)\) n/a 188 2
3330.2.bx \(\chi_{3330}(751, \cdot)\) n/a 304 2
3330.2.ca \(\chi_{3330}(571, \cdot)\) n/a 912 6
3330.2.cb \(\chi_{3330}(181, \cdot)\) n/a 372 6
3330.2.cc \(\chi_{3330}(601, \cdot)\) n/a 912 6
3330.2.cd \(\chi_{3330}(569, \cdot)\) n/a 912 4
3330.2.cg \(\chi_{3330}(191, \cdot)\) n/a 608 4
3330.2.ch \(\chi_{3330}(1361, \cdot)\) n/a 608 4
3330.2.ck \(\chi_{3330}(251, \cdot)\) n/a 224 4
3330.2.cl \(\chi_{3330}(1207, \cdot)\) n/a 380 4
3330.2.cm \(\chi_{3330}(233, \cdot)\) n/a 304 4
3330.2.cn \(\chi_{3330}(2267, \cdot)\) n/a 304 4
3330.2.co \(\chi_{3330}(1657, \cdot)\) n/a 380 4
3330.2.db \(\chi_{3330}(547, \cdot)\) n/a 912 4
3330.2.dc \(\chi_{3330}(1363, \cdot)\) n/a 912 4
3330.2.dd \(\chi_{3330}(97, \cdot)\) n/a 912 4
3330.2.de \(\chi_{3330}(1037, \cdot)\) n/a 864 4
3330.2.df \(\chi_{3330}(677, \cdot)\) n/a 912 4
3330.2.dg \(\chi_{3330}(767, \cdot)\) n/a 912 4
3330.2.dh \(\chi_{3330}(137, \cdot)\) n/a 912 4
3330.2.di \(\chi_{3330}(47, \cdot)\) n/a 912 4
3330.2.dj \(\chi_{3330}(443, \cdot)\) n/a 912 4
3330.2.dk \(\chi_{3330}(193, \cdot)\) n/a 912 4
3330.2.dl \(\chi_{3330}(43, \cdot)\) n/a 912 4
3330.2.dm \(\chi_{3330}(637, \cdot)\) n/a 912 4
3330.2.ds \(\chi_{3330}(1289, \cdot)\) n/a 912 4
3330.2.dt \(\chi_{3330}(29, \cdot)\) n/a 912 4
3330.2.dw \(\chi_{3330}(1799, \cdot)\) n/a 304 4
3330.2.dx \(\chi_{3330}(911, \cdot)\) n/a 608 4
3330.2.ed \(\chi_{3330}(289, \cdot)\) n/a 576 6
3330.2.ee \(\chi_{3330}(139, \cdot)\) n/a 1368 6
3330.2.ef \(\chi_{3330}(49, \cdot)\) n/a 1368 6
3330.2.eg \(\chi_{3330}(379, \cdot)\) n/a 564 6
3330.2.eh \(\chi_{3330}(361, \cdot)\) n/a 372 6
3330.2.ei \(\chi_{3330}(151, \cdot)\) n/a 912 6
3330.2.er \(\chi_{3330}(691, \cdot)\) n/a 912 6
3330.2.es \(\chi_{3330}(229, \cdot)\) n/a 1368 6
3330.2.et \(\chi_{3330}(169, \cdot)\) n/a 1368 6
3330.2.eu \(\chi_{3330}(13, \cdot)\) n/a 2736 12
3330.2.ev \(\chi_{3330}(77, \cdot)\) n/a 2736 12
3330.2.ey \(\chi_{3330}(83, \cdot)\) n/a 2736 12
3330.2.ez \(\chi_{3330}(283, \cdot)\) n/a 2736 12
3330.2.fe \(\chi_{3330}(131, \cdot)\) n/a 1824 12
3330.2.ff \(\chi_{3330}(89, \cdot)\) n/a 912 12
3330.2.fg \(\chi_{3330}(161, \cdot)\) n/a 576 12
3330.2.fh \(\chi_{3330}(59, \cdot)\) n/a 2736 12
3330.2.fm \(\chi_{3330}(457, \cdot)\) n/a 2736 12
3330.2.fn \(\chi_{3330}(163, \cdot)\) n/a 1140 12
3330.2.fo \(\chi_{3330}(527, \cdot)\) n/a 2736 12
3330.2.fp \(\chi_{3330}(53, \cdot)\) n/a 912 12
3330.2.fu \(\chi_{3330}(287, \cdot)\) n/a 912 12
3330.2.fv \(\chi_{3330}(263, \cdot)\) n/a 2736 12
3330.2.fw \(\chi_{3330}(217, \cdot)\) n/a 1140 12
3330.2.fx \(\chi_{3330}(277, \cdot)\) n/a 2736 12
3330.2.ga \(\chi_{3330}(479, \cdot)\) n/a 2736 12
3330.2.gb \(\chi_{3330}(281, \cdot)\) n/a 1824 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3330))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3330)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1665))\)\(^{\oplus 2}\)