↑

Properties

Label 2730.2
Level 2730
Weight 2
Dimension 42007
Nonzero newspaces 100
Sturm bound 774144
Trace bound 21

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2730 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(774144\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2730))\).

Total New Old
Modular forms 198144 42007 156137
Cusp forms 188929 42007 146922
Eisenstein series 9215 0 9215

Trace form

\( 42007 q - q^{2} - 17 q^{3} - 17 q^{4} - 41 q^{5} - 33 q^{6} - 81 q^{7} - 25 q^{8} - 49 q^{9} + O(q^{10}) \) \( 42007 q - q^{2} - 17 q^{3} - 17 q^{4} - 41 q^{5} - 33 q^{6} - 81 q^{7} - 25 q^{8} - 49 q^{9} - 69 q^{10} - 140 q^{11} - q^{12} - 193 q^{13} - 17 q^{14} - 9 q^{15} - 33 q^{16} - 90 q^{17} + 55 q^{18} - 244 q^{19} + 3 q^{20} - q^{21} + 20 q^{22} - 72 q^{23} + 15 q^{24} + 15 q^{25} + 23 q^{26} - 17 q^{27} + 47 q^{28} + 42 q^{29} + 111 q^{30} - 32 q^{31} - q^{32} + 212 q^{33} + 142 q^{34} + 199 q^{35} + 159 q^{36} + 258 q^{37} + 124 q^{38} + 295 q^{39} + 23 q^{40} + 94 q^{41} + 127 q^{42} - 44 q^{43} + 20 q^{44} + 211 q^{45} + 72 q^{46} + 15 q^{48} - 65 q^{49} - 29 q^{50} + 174 q^{51} + 71 q^{52} + 90 q^{53} + 207 q^{54} + 412 q^{55} + 15 q^{56} + 188 q^{57} + 298 q^{58} + 292 q^{59} + 143 q^{60} + 266 q^{61} + 256 q^{62} + 319 q^{63} + 7 q^{64} + 623 q^{65} + 276 q^{66} + 764 q^{67} + 54 q^{68} + 616 q^{69} + 215 q^{70} + 408 q^{71} + 15 q^{72} + 678 q^{73} + 386 q^{74} + 735 q^{75} + 396 q^{76} + 900 q^{77} + 311 q^{78} + 1136 q^{79} - 5 q^{80} + 223 q^{81} + 590 q^{82} + 588 q^{83} + 191 q^{84} + 450 q^{85} + 324 q^{86} + 578 q^{87} - 28 q^{88} + 710 q^{89} - 73 q^{90} + 943 q^{91} + 360 q^{92} + 176 q^{93} + 752 q^{94} + 244 q^{95} - q^{96} + 1102 q^{97} + 479 q^{98} - 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2730))\)

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
2730.2.a \(\chi_{2730}(1, \cdot)\) 2730.2.a.a 1 1
2730.2.a.b 1
2730.2.a.c 1
2730.2.a.d 1
2730.2.a.e 1
2730.2.a.f 1
2730.2.a.g 1
2730.2.a.h 1
2730.2.a.i 1
2730.2.a.j 1
2730.2.a.k 1
2730.2.a.l 1
2730.2.a.m 1
2730.2.a.n 1
2730.2.a.o 1
2730.2.a.p 1
2730.2.a.q 1
2730.2.a.r 1
2730.2.a.s 1
2730.2.a.t 1
2730.2.a.u 1
2730.2.a.v 1
2730.2.a.w 1
2730.2.a.x 1
2730.2.a.y 1
2730.2.a.z 1
2730.2.a.ba 1
2730.2.a.bb 1
2730.2.a.bc 1
2730.2.a.bd 1
2730.2.a.be 2
2730.2.a.bf 2
2730.2.a.bg 2
2730.2.a.bh 2
2730.2.a.bi 2
2730.2.a.bj 2
2730.2.a.bk 2
2730.2.a.bl 3
2730.2.b \(\chi_{2730}(1429, \cdot)\) 2730.2.b.a 2 1
2730.2.b.b 2
2730.2.b.c 2
2730.2.b.d 2
2730.2.b.e 2
2730.2.b.f 2
2730.2.b.g 18
2730.2.b.h 18
2730.2.b.i 20
2730.2.b.j 20
2730.2.c \(\chi_{2730}(209, \cdot)\) n/a 192 1
2730.2.f \(\chi_{2730}(1301, \cdot)\) n/a 128 1
2730.2.g \(\chi_{2730}(2521, \cdot)\) 2730.2.g.a 2 1
2730.2.g.b 2
2730.2.g.c 2
2730.2.g.d 2
2730.2.g.e 2
2730.2.g.f 2
2730.2.g.g 2
2730.2.g.h 2
2730.2.g.i 2
2730.2.g.j 2
2730.2.g.k 2
2730.2.g.l 2
2730.2.g.m 2
2730.2.g.n 4
2730.2.g.o 4
2730.2.g.p 4
2730.2.g.q 4
2730.2.g.r 6
2730.2.g.s 8
2730.2.l \(\chi_{2730}(1639, \cdot)\) 2730.2.l.a 2 1
2730.2.l.b 2
2730.2.l.c 2
2730.2.l.d 2
2730.2.l.e 2
2730.2.l.f 2
2730.2.l.g 2
2730.2.l.h 2
2730.2.l.i 2
2730.2.l.j 2
2730.2.l.k 2
2730.2.l.l 2
2730.2.l.m 2
2730.2.l.n 4
2730.2.l.o 4
2730.2.l.p 8
2730.2.l.q 8
2730.2.l.r 10
2730.2.l.s 12
2730.2.m \(\chi_{2730}(2729, \cdot)\) n/a 224 1
2730.2.p \(\chi_{2730}(1091, \cdot)\) n/a 144 1
2730.2.q \(\chi_{2730}(211, \cdot)\) n/a 112 2
2730.2.r \(\chi_{2730}(781, \cdot)\) n/a 128 2
2730.2.s \(\chi_{2730}(1381, \cdot)\) n/a 152 2
2730.2.t \(\chi_{2730}(991, \cdot)\) n/a 152 2
2730.2.u \(\chi_{2730}(727, \cdot)\) n/a 224 2
2730.2.v \(\chi_{2730}(1457, \cdot)\) n/a 288 2
2730.2.y \(\chi_{2730}(239, \cdot)\) n/a 336 2
2730.2.bb \(\chi_{2730}(1399, \cdot)\) n/a 224 2
2730.2.bc \(\chi_{2730}(463, \cdot)\) n/a 168 2
2730.2.bf \(\chi_{2730}(1513, \cdot)\) n/a 168 2
2730.2.bg \(\chi_{2730}(1763, \cdot)\) n/a 448 2
2730.2.bj \(\chi_{2730}(83, \cdot)\) n/a 448 2
2730.2.bl \(\chi_{2730}(811, \cdot)\) n/a 160 2
2730.2.bm \(\chi_{2730}(281, \cdot)\) n/a 224 2
2730.2.bq \(\chi_{2730}(937, \cdot)\) n/a 192 2
2730.2.br \(\chi_{2730}(1247, \cdot)\) n/a 336 2
2730.2.bs \(\chi_{2730}(121, \cdot)\) n/a 152 2
2730.2.bt \(\chi_{2730}(731, \cdot)\) n/a 296 2
2730.2.bw \(\chi_{2730}(2369, \cdot)\) n/a 448 2
2730.2.bx \(\chi_{2730}(1759, \cdot)\) n/a 224 2
2730.2.ca \(\chi_{2730}(289, \cdot)\) n/a 224 2
2730.2.cb \(\chi_{2730}(1109, \cdot)\) n/a 448 2
2730.2.ce \(\chi_{2730}(311, \cdot)\) n/a 304 2
2730.2.cf \(\chi_{2730}(251, \cdot)\) n/a 304 2
2730.2.ck \(\chi_{2730}(1559, \cdot)\) n/a 448 2
2730.2.cl \(\chi_{2730}(1889, \cdot)\) n/a 448 2
2730.2.cm \(\chi_{2730}(1849, \cdot)\) n/a 160 2
2730.2.cn \(\chi_{2730}(79, \cdot)\) n/a 192 2
2730.2.cs \(\chi_{2730}(2201, \cdot)\) n/a 296 2
2730.2.cx \(\chi_{2730}(1369, \cdot)\) n/a 224 2
2730.2.cy \(\chi_{2730}(269, \cdot)\) n/a 448 2
2730.2.dd \(\chi_{2730}(1681, \cdot)\) n/a 112 2
2730.2.de \(\chi_{2730}(571, \cdot)\) n/a 144 2
2730.2.df \(\chi_{2730}(131, \cdot)\) n/a 256 2
2730.2.dg \(\chi_{2730}(1511, \cdot)\) n/a 304 2
2730.2.dl \(\chi_{2730}(1769, \cdot)\) n/a 384 2
2730.2.dm \(\chi_{2730}(419, \cdot)\) n/a 448 2
2730.2.dn \(\chi_{2730}(589, \cdot)\) n/a 176 2
2730.2.do \(\chi_{2730}(2209, \cdot)\) n/a 224 2
2730.2.dr \(\chi_{2730}(341, \cdot)\) n/a 296 2
2730.2.ds \(\chi_{2730}(751, \cdot)\) n/a 152 2
2730.2.dv \(\chi_{2730}(101, \cdot)\) n/a 296 2
2730.2.dy \(\chi_{2730}(719, \cdot)\) n/a 448 2
2730.2.dz \(\chi_{2730}(919, \cdot)\) n/a 224 2
2730.2.ea \(\chi_{2730}(263, \cdot)\) n/a 896 4
2730.2.eb \(\chi_{2730}(283, \cdot)\) n/a 448 4
2730.2.ee \(\chi_{2730}(157, \cdot)\) n/a 384 4
2730.2.ef \(\chi_{2730}(407, \cdot)\) n/a 672 4
2730.2.eg \(\chi_{2730}(23, \cdot)\) n/a 896 4
2730.2.eh \(\chi_{2730}(1147, \cdot)\) n/a 448 4
2730.2.ei \(\chi_{2730}(523, \cdot)\) n/a 448 4
2730.2.ej \(\chi_{2730}(233, \cdot)\) n/a 896 4
2730.2.er \(\chi_{2730}(1229, \cdot)\) n/a 896 4
2730.2.es \(\chi_{2730}(409, \cdot)\) n/a 448 4
2730.2.eu \(\chi_{2730}(1061, \cdot)\) n/a 608 4
2730.2.ex \(\chi_{2730}(71, \cdot)\) n/a 448 4
2730.2.ey \(\chi_{2730}(11, \cdot)\) n/a 592 4
2730.2.fb \(\chi_{2730}(661, \cdot)\) n/a 304 4
2730.2.fc \(\chi_{2730}(1021, \cdot)\) n/a 288 4
2730.2.ff \(\chi_{2730}(31, \cdot)\) n/a 288 4
2730.2.fg \(\chi_{2730}(697, \cdot)\) n/a 448 4
2730.2.fj \(\chi_{2730}(1243, \cdot)\) n/a 448 4
2730.2.fl \(\chi_{2730}(227, \cdot)\) n/a 896 4
2730.2.fn \(\chi_{2730}(353, \cdot)\) n/a 896 4
2730.2.fp \(\chi_{2730}(167, \cdot)\) n/a 896 4
2730.2.fq \(\chi_{2730}(293, \cdot)\) n/a 896 4
2730.2.fs \(\chi_{2730}(1853, \cdot)\) n/a 896 4
2730.2.fu \(\chi_{2730}(773, \cdot)\) n/a 896 4
2730.2.fx \(\chi_{2730}(457, \cdot)\) n/a 448 4
2730.2.fz \(\chi_{2730}(613, \cdot)\) n/a 448 4
2730.2.gb \(\chi_{2730}(253, \cdot)\) n/a 336 4
2730.2.gc \(\chi_{2730}(1723, \cdot)\) n/a 336 4
2730.2.ge \(\chi_{2730}(67, \cdot)\) n/a 448 4
2730.2.gg \(\chi_{2730}(37, \cdot)\) n/a 448 4
2730.2.gi \(\chi_{2730}(47, \cdot)\) n/a 896 4
2730.2.gl \(\chi_{2730}(593, \cdot)\) n/a 896 4
2730.2.gn \(\chi_{2730}(349, \cdot)\) n/a 448 4
2730.2.go \(\chi_{2730}(19, \cdot)\) n/a 448 4
2730.2.gr \(\chi_{2730}(229, \cdot)\) n/a 448 4
2730.2.gs \(\chi_{2730}(359, \cdot)\) n/a 896 4
2730.2.gv \(\chi_{2730}(149, \cdot)\) n/a 896 4
2730.2.gw \(\chi_{2730}(449, \cdot)\) n/a 672 4
2730.2.gy \(\chi_{2730}(241, \cdot)\) n/a 304 4
2730.2.hb \(\chi_{2730}(401, \cdot)\) n/a 592 4
2730.2.hi \(\chi_{2730}(103, \cdot)\) n/a 448 4
2730.2.hj \(\chi_{2730}(107, \cdot)\) n/a 896 4
2730.2.hk \(\chi_{2730}(113, \cdot)\) n/a 672 4
2730.2.hl \(\chi_{2730}(1837, \cdot)\) n/a 448 4
2730.2.hm \(\chi_{2730}(433, \cdot)\) n/a 448 4
2730.2.hn \(\chi_{2730}(53, \cdot)\) n/a 768 4
2730.2.hq \(\chi_{2730}(1577, \cdot)\) n/a 896 4
2730.2.hr \(\chi_{2730}(367, \cdot)\) n/a 448 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2730))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2730)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(910))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1365))\)\(^{\oplus 2}\)