↑

Properties

Label 3360.2
Level 3360
Weight 2
Dimension 108696
Nonzero newspaces 80
Sturm bound 1179648
Trace bound 71

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(1179648\)
Trace bound: \(71\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3360))\).

Total New Old
Modular forms 301056 109896 191160
Cusp forms 288769 108696 180073
Eisenstein series 12287 1200 11087

Trace form

\( 108696 q - 20 q^{3} - 64 q^{4} + 8 q^{5} - 96 q^{6} - 56 q^{7} - 32 q^{9} + O(q^{10}) \) \( 108696 q - 20 q^{3} - 64 q^{4} + 8 q^{5} - 96 q^{6} - 56 q^{7} - 32 q^{9} - 128 q^{10} - 96 q^{12} - 112 q^{13} - 64 q^{14} - 108 q^{15} - 352 q^{16} - 64 q^{17} - 64 q^{18} - 88 q^{19} - 64 q^{20} - 152 q^{21} - 256 q^{22} - 96 q^{23} + 16 q^{24} - 160 q^{25} + 160 q^{26} - 176 q^{27} - 16 q^{29} + 48 q^{30} - 392 q^{31} + 160 q^{32} - 136 q^{33} + 32 q^{34} - 96 q^{35} - 32 q^{36} - 144 q^{37} + 160 q^{38} - 184 q^{39} - 16 q^{40} - 96 q^{41} + 80 q^{42} - 288 q^{43} + 32 q^{44} - 56 q^{45} - 192 q^{46} - 144 q^{47} + 176 q^{48} - 184 q^{49} + 48 q^{50} - 148 q^{51} + 128 q^{52} - 272 q^{53} + 176 q^{54} - 112 q^{55} + 112 q^{56} - 176 q^{57} + 224 q^{58} + 64 q^{59} + 200 q^{60} - 624 q^{61} + 192 q^{62} - 92 q^{63} + 320 q^{64} + 48 q^{65} + 256 q^{66} + 104 q^{67} + 416 q^{68} - 192 q^{69} + 192 q^{70} + 240 q^{71} + 208 q^{72} + 576 q^{74} + 98 q^{75} + 320 q^{76} + 64 q^{77} + 272 q^{78} + 200 q^{79} + 528 q^{80} + 64 q^{81} + 256 q^{82} + 160 q^{83} + 16 q^{85} + 256 q^{86} + 344 q^{87} + 288 q^{88} + 256 q^{89} + 168 q^{90} + 48 q^{91} + 352 q^{92} + 304 q^{93} + 608 q^{94} + 200 q^{95} + 80 q^{96} + 320 q^{97} + 608 q^{98} + 440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3360))\)

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
3360.2.a \(\chi_{3360}(1, \cdot)\) 3360.2.a.a 1 1
3360.2.a.b 1
3360.2.a.c 1
3360.2.a.d 1
3360.2.a.e 1
3360.2.a.f 1
3360.2.a.g 1
3360.2.a.h 1
3360.2.a.i 1
3360.2.a.j 1
3360.2.a.k 1
3360.2.a.l 1
3360.2.a.m 1
3360.2.a.n 1
3360.2.a.o 1
3360.2.a.p 1
3360.2.a.q 1
3360.2.a.r 1
3360.2.a.s 1
3360.2.a.t 1
3360.2.a.u 1
3360.2.a.v 1
3360.2.a.w 1
3360.2.a.x 1
3360.2.a.y 1
3360.2.a.z 1
3360.2.a.ba 2
3360.2.a.bb 2
3360.2.a.bc 2
3360.2.a.bd 2
3360.2.a.be 2
3360.2.a.bf 2
3360.2.a.bg 2
3360.2.a.bh 2
3360.2.a.bi 3
3360.2.a.bj 3
3360.2.d \(\chi_{3360}(2911, \cdot)\) 3360.2.d.a 16 1
3360.2.d.b 16
3360.2.d.c 16
3360.2.d.d 16
3360.2.e \(\chi_{3360}(911, \cdot)\) 3360.2.e.a 4 1
3360.2.e.b 4
3360.2.e.c 44
3360.2.e.d 44
3360.2.f \(\chi_{3360}(2561, \cdot)\) n/a 128 1
3360.2.g \(\chi_{3360}(1681, \cdot)\) 3360.2.g.a 8 1
3360.2.g.b 12
3360.2.g.c 12
3360.2.g.d 16
3360.2.j \(\chi_{3360}(1009, \cdot)\) 3360.2.j.a 2 1
3360.2.j.b 2
3360.2.j.c 2
3360.2.j.d 2
3360.2.j.e 32
3360.2.j.f 32
3360.2.k \(\chi_{3360}(1889, \cdot)\) n/a 192 1
3360.2.p \(\chi_{3360}(239, \cdot)\) n/a 144 1
3360.2.q \(\chi_{3360}(2239, \cdot)\) 3360.2.q.a 48 1
3360.2.q.b 48
3360.2.t \(\chi_{3360}(2689, \cdot)\) 3360.2.t.a 2 1
3360.2.t.b 2
3360.2.t.c 2
3360.2.t.d 2
3360.2.t.e 2
3360.2.t.f 2
3360.2.t.g 4
3360.2.t.h 6
3360.2.t.i 6
3360.2.t.j 8
3360.2.t.k 8
3360.2.t.l 8
3360.2.t.m 10
3360.2.t.n 10
3360.2.u \(\chi_{3360}(209, \cdot)\) n/a 184 1
3360.2.v \(\chi_{3360}(1919, \cdot)\) n/a 144 1
3360.2.w \(\chi_{3360}(559, \cdot)\) 3360.2.w.a 48 1
3360.2.w.b 48
3360.2.z \(\chi_{3360}(1231, \cdot)\) 3360.2.z.a 4 1
3360.2.z.b 4
3360.2.z.c 28
3360.2.z.d 28
3360.2.ba \(\chi_{3360}(2591, \cdot)\) 3360.2.ba.a 4 1
3360.2.ba.b 4
3360.2.ba.c 20
3360.2.ba.d 20
3360.2.ba.e 24
3360.2.ba.f 24
3360.2.bf \(\chi_{3360}(881, \cdot)\) n/a 128 1
3360.2.bg \(\chi_{3360}(961, \cdot)\) n/a 128 2
3360.2.bj \(\chi_{3360}(433, \cdot)\) n/a 192 2
3360.2.bk \(\chi_{3360}(1793, \cdot)\) n/a 288 2
3360.2.bl \(\chi_{3360}(127, \cdot)\) n/a 144 2
3360.2.bm \(\chi_{3360}(1007, \cdot)\) n/a 368 2
3360.2.bp \(\chi_{3360}(967, \cdot)\) None 0 2
3360.2.bs \(\chi_{3360}(937, \cdot)\) None 0 2
3360.2.bu \(\chi_{3360}(2297, \cdot)\) None 0 2
3360.2.bv \(\chi_{3360}(1847, \cdot)\) None 0 2
3360.2.bx \(\chi_{3360}(1049, \cdot)\) None 0 2
3360.2.ca \(\chi_{3360}(71, \cdot)\) None 0 2
3360.2.cb \(\chi_{3360}(169, \cdot)\) None 0 2
3360.2.ce \(\chi_{3360}(391, \cdot)\) None 0 2
3360.2.cg \(\chi_{3360}(841, \cdot)\) None 0 2
3360.2.ch \(\chi_{3360}(1399, \cdot)\) None 0 2
3360.2.ck \(\chi_{3360}(41, \cdot)\) None 0 2
3360.2.cl \(\chi_{3360}(1079, \cdot)\) None 0 2
3360.2.co \(\chi_{3360}(2617, \cdot)\) None 0 2
3360.2.cp \(\chi_{3360}(2647, \cdot)\) None 0 2
3360.2.cr \(\chi_{3360}(167, \cdot)\) None 0 2
3360.2.cu \(\chi_{3360}(617, \cdot)\) None 0 2
3360.2.cx \(\chi_{3360}(463, \cdot)\) n/a 144 2
3360.2.cy \(\chi_{3360}(1343, \cdot)\) n/a 384 2
3360.2.cz \(\chi_{3360}(97, \cdot)\) n/a 192 2
3360.2.da \(\chi_{3360}(113, \cdot)\) n/a 288 2
3360.2.df \(\chi_{3360}(1039, \cdot)\) n/a 192 2
3360.2.dg \(\chi_{3360}(1439, \cdot)\) n/a 384 2
3360.2.dh \(\chi_{3360}(689, \cdot)\) n/a 368 2
3360.2.di \(\chi_{3360}(289, \cdot)\) n/a 192 2
3360.2.dl \(\chi_{3360}(1361, \cdot)\) n/a 256 2
3360.2.dq \(\chi_{3360}(191, \cdot)\) n/a 256 2
3360.2.dr \(\chi_{3360}(271, \cdot)\) n/a 128 2
3360.2.du \(\chi_{3360}(1201, \cdot)\) n/a 128 2
3360.2.dv \(\chi_{3360}(1601, \cdot)\) n/a 256 2
3360.2.dw \(\chi_{3360}(431, \cdot)\) n/a 256 2
3360.2.dx \(\chi_{3360}(31, \cdot)\) n/a 128 2
3360.2.ea \(\chi_{3360}(1279, \cdot)\) n/a 192 2
3360.2.eb \(\chi_{3360}(1199, \cdot)\) n/a 368 2
3360.2.eg \(\chi_{3360}(929, \cdot)\) n/a 384 2
3360.2.eh \(\chi_{3360}(529, \cdot)\) n/a 192 2
3360.2.ei \(\chi_{3360}(461, \cdot)\) n/a 2048 4
3360.2.ek \(\chi_{3360}(659, \cdot)\) n/a 2304 4
3360.2.en \(\chi_{3360}(421, \cdot)\) n/a 768 4
3360.2.ep \(\chi_{3360}(139, \cdot)\) n/a 1536 4
3360.2.es \(\chi_{3360}(43, \cdot)\) n/a 1152 4
3360.2.et \(\chi_{3360}(13, \cdot)\) n/a 1536 4
3360.2.ew \(\chi_{3360}(83, \cdot)\) n/a 3040 4
3360.2.ex \(\chi_{3360}(533, \cdot)\) n/a 2304 4
3360.2.ey \(\chi_{3360}(883, \cdot)\) n/a 1152 4
3360.2.ez \(\chi_{3360}(853, \cdot)\) n/a 1536 4
3360.2.fc \(\chi_{3360}(923, \cdot)\) n/a 3040 4
3360.2.fd \(\chi_{3360}(197, \cdot)\) n/a 2304 4
3360.2.fh \(\chi_{3360}(491, \cdot)\) n/a 1536 4
3360.2.fj \(\chi_{3360}(629, \cdot)\) n/a 3040 4
3360.2.fk \(\chi_{3360}(811, \cdot)\) n/a 1024 4
3360.2.fm \(\chi_{3360}(589, \cdot)\) n/a 1152 4
3360.2.fo \(\chi_{3360}(977, \cdot)\) n/a 736 4
3360.2.fp \(\chi_{3360}(577, \cdot)\) n/a 384 4
3360.2.fu \(\chi_{3360}(383, \cdot)\) n/a 768 4
3360.2.fv \(\chi_{3360}(1327, \cdot)\) n/a 384 4
3360.2.fw \(\chi_{3360}(887, \cdot)\) None 0 4
3360.2.fz \(\chi_{3360}(233, \cdot)\) None 0 4
3360.2.gb \(\chi_{3360}(313, \cdot)\) None 0 4
3360.2.gc \(\chi_{3360}(487, \cdot)\) None 0 4
3360.2.ge \(\chi_{3360}(521, \cdot)\) None 0 4
3360.2.gh \(\chi_{3360}(359, \cdot)\) None 0 4
3360.2.gi \(\chi_{3360}(121, \cdot)\) None 0 4
3360.2.gl \(\chi_{3360}(199, \cdot)\) None 0 4
3360.2.gn \(\chi_{3360}(1129, \cdot)\) None 0 4
3360.2.go \(\chi_{3360}(871, \cdot)\) None 0 4
3360.2.gr \(\chi_{3360}(89, \cdot)\) None 0 4
3360.2.gs \(\chi_{3360}(1031, \cdot)\) None 0 4
3360.2.gv \(\chi_{3360}(137, \cdot)\) None 0 4
3360.2.gw \(\chi_{3360}(647, \cdot)\) None 0 4
3360.2.gy \(\chi_{3360}(247, \cdot)\) None 0 4
3360.2.hb \(\chi_{3360}(73, \cdot)\) None 0 4
3360.2.hc \(\chi_{3360}(47, \cdot)\) n/a 736 4
3360.2.hd \(\chi_{3360}(1087, \cdot)\) n/a 384 4
3360.2.hi \(\chi_{3360}(737, \cdot)\) n/a 768 4
3360.2.hj \(\chi_{3360}(817, \cdot)\) n/a 384 4
3360.2.hk \(\chi_{3360}(109, \cdot)\) n/a 3072 8
3360.2.hm \(\chi_{3360}(451, \cdot)\) n/a 2048 8
3360.2.hp \(\chi_{3360}(269, \cdot)\) n/a 6080 8
3360.2.hr \(\chi_{3360}(11, \cdot)\) n/a 4096 8
3360.2.hu \(\chi_{3360}(653, \cdot)\) n/a 6080 8
3360.2.hv \(\chi_{3360}(227, \cdot)\) n/a 6080 8
3360.2.hy \(\chi_{3360}(157, \cdot)\) n/a 3072 8
3360.2.hz \(\chi_{3360}(163, \cdot)\) n/a 3072 8
3360.2.ia \(\chi_{3360}(53, \cdot)\) n/a 6080 8
3360.2.ib \(\chi_{3360}(563, \cdot)\) n/a 6080 8
3360.2.ie \(\chi_{3360}(493, \cdot)\) n/a 3072 8
3360.2.if \(\chi_{3360}(67, \cdot)\) n/a 3072 8
3360.2.ij \(\chi_{3360}(19, \cdot)\) n/a 3072 8
3360.2.il \(\chi_{3360}(541, \cdot)\) n/a 2048 8
3360.2.im \(\chi_{3360}(179, \cdot)\) n/a 6080 8
3360.2.io \(\chi_{3360}(101, \cdot)\) n/a 4096 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1680))\)\(^{\oplus 2}\)