Properties

Label 3549.2
Level 3549
Weight 2
Dimension 320608
Nonzero newspaces 60
Sturm bound 1817088
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1817088\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3549))\).

Total New Old
Modular forms 459744 324700 135044
Cusp forms 448801 320608 128193
Eisenstein series 10943 4092 6851

Trace form

\( 320608q - 6q^{2} - 268q^{3} - 540q^{4} - 6q^{5} - 264q^{6} - 658q^{7} + 60q^{8} - 254q^{9} + O(q^{10}) \) \( 320608q - 6q^{2} - 268q^{3} - 540q^{4} - 6q^{5} - 264q^{6} - 658q^{7} + 60q^{8} - 254q^{9} - 420q^{10} + 42q^{11} - 164q^{12} - 528q^{13} + 48q^{14} - 624q^{15} - 400q^{16} + 48q^{17} - 174q^{18} - 394q^{19} + 216q^{20} - 282q^{21} - 1128q^{22} + 72q^{23} - 132q^{24} - 386q^{25} + 120q^{26} - 358q^{27} - 482q^{28} + 96q^{29} - 180q^{30} - 458q^{31} + 180q^{32} - 246q^{33} - 384q^{34} + 42q^{35} - 796q^{36} - 540q^{37} - 66q^{38} - 320q^{39} - 912q^{40} + 108q^{41} - 306q^{42} - 1112q^{43} + 156q^{44} - 318q^{45} - 120q^{46} + 150q^{47} - 160q^{48} - 486q^{49} + 360q^{50} - 72q^{51} - 276q^{52} + 324q^{53} - 78q^{54} - 72q^{55} + 342q^{56} - 360q^{57} - 24q^{58} + 300q^{59} + 108q^{60} - 134q^{61} + 468q^{62} - 264q^{63} - 744q^{64} + 180q^{65} - 492q^{66} - 342q^{67} + 240q^{68} - 264q^{69} - 432q^{70} + 12q^{71} - 300q^{72} - 520q^{73} - 102q^{74} - 470q^{75} - 988q^{76} - 312q^{77} - 972q^{78} - 1378q^{79} - 792q^{80} - 434q^{81} - 1380q^{82} - 372q^{83} - 912q^{84} - 1920q^{85} - 330q^{86} - 636q^{87} - 1608q^{88} - 216q^{89} - 528q^{90} - 884q^{91} - 648q^{92} - 384q^{93} - 1236q^{94} - 30q^{95} - 732q^{96} - 956q^{97} - 264q^{98} - 360q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3549))\)

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
3549.2.a \(\chi_{3549}(1, \cdot)\) 3549.2.a.a 1 1
3549.2.a.b 1
3549.2.a.c 1
3549.2.a.d 1
3549.2.a.e 1
3549.2.a.f 2
3549.2.a.g 3
3549.2.a.h 3
3549.2.a.i 3
3549.2.a.j 3
3549.2.a.k 3
3549.2.a.l 3
3549.2.a.m 3
3549.2.a.n 3
3549.2.a.o 3
3549.2.a.p 3
3549.2.a.q 3
3549.2.a.r 3
3549.2.a.s 3
3549.2.a.t 3
3549.2.a.u 3
3549.2.a.v 4
3549.2.a.w 4
3549.2.a.x 4
3549.2.a.y 6
3549.2.a.z 6
3549.2.a.ba 8
3549.2.a.bb 8
3549.2.a.bc 8
3549.2.a.bd 8
3549.2.a.be 9
3549.2.a.bf 9
3549.2.a.bg 15
3549.2.a.bh 15
3549.2.c \(\chi_{3549}(337, \cdot)\) n/a 152 1
3549.2.e \(\chi_{3549}(3212, \cdot)\) n/a 392 1
3549.2.g \(\chi_{3549}(3548, \cdot)\) n/a 392 1
3549.2.i \(\chi_{3549}(508, \cdot)\) n/a 414 2
3549.2.j \(\chi_{3549}(991, \cdot)\) n/a 410 2
3549.2.k \(\chi_{3549}(22, \cdot)\) n/a 312 2
3549.2.l \(\chi_{3549}(529, \cdot)\) n/a 410 2
3549.2.n \(\chi_{3549}(239, \cdot)\) n/a 616 2
3549.2.p \(\chi_{3549}(1084, \cdot)\) n/a 408 2
3549.2.r \(\chi_{3549}(1160, \cdot)\) n/a 782 2
3549.2.t \(\chi_{3549}(823, \cdot)\) n/a 410 2
3549.2.u \(\chi_{3549}(3065, \cdot)\) n/a 780 2
3549.2.y \(\chi_{3549}(992, \cdot)\) n/a 782 2
3549.2.ba \(\chi_{3549}(1013, \cdot)\) n/a 780 2
3549.2.bd \(\chi_{3549}(316, \cdot)\) n/a 304 2
3549.2.bf \(\chi_{3549}(698, \cdot)\) n/a 782 2
3549.2.bh \(\chi_{3549}(677, \cdot)\) n/a 782 2
3549.2.bj \(\chi_{3549}(844, \cdot)\) n/a 412 2
3549.2.bl \(\chi_{3549}(361, \cdot)\) n/a 410 2
3549.2.bn \(\chi_{3549}(146, \cdot)\) n/a 780 2
3549.2.br \(\chi_{3549}(530, \cdot)\) n/a 782 2
3549.2.bt \(\chi_{3549}(418, \cdot)\) n/a 820 4
3549.2.bv \(\chi_{3549}(1094, \cdot)\) n/a 1564 4
3549.2.bw \(\chi_{3549}(695, \cdot)\) n/a 1564 4
3549.2.by \(\chi_{3549}(1441, \cdot)\) n/a 824 4
3549.2.bz \(\chi_{3549}(577, \cdot)\) n/a 824 4
3549.2.cc \(\chi_{3549}(596, \cdot)\) n/a 1232 4
3549.2.cd \(\chi_{3549}(746, \cdot)\) n/a 1560 4
3549.2.cg \(\chi_{3549}(19, \cdot)\) n/a 820 4
3549.2.ci \(\chi_{3549}(274, \cdot)\) n/a 2160 12
3549.2.ck \(\chi_{3549}(272, \cdot)\) n/a 5760 12
3549.2.cm \(\chi_{3549}(209, \cdot)\) n/a 5760 12
3549.2.co \(\chi_{3549}(64, \cdot)\) n/a 2208 12
3549.2.cq \(\chi_{3549}(16, \cdot)\) n/a 5832 24
3549.2.cr \(\chi_{3549}(211, \cdot)\) n/a 4320 24
3549.2.cs \(\chi_{3549}(100, \cdot)\) n/a 5832 24
3549.2.ct \(\chi_{3549}(79, \cdot)\) n/a 5808 24
3549.2.cu \(\chi_{3549}(34, \cdot)\) n/a 5856 24
3549.2.cw \(\chi_{3549}(8, \cdot)\) n/a 8736 24
3549.2.cy \(\chi_{3549}(17, \cdot)\) n/a 11544 24
3549.2.dc \(\chi_{3549}(230, \cdot)\) n/a 11568 24
3549.2.de \(\chi_{3549}(88, \cdot)\) n/a 5832 24
3549.2.dg \(\chi_{3549}(25, \cdot)\) n/a 5808 24
3549.2.di \(\chi_{3549}(131, \cdot)\) n/a 11568 24
3549.2.dk \(\chi_{3549}(152, \cdot)\) n/a 11544 24
3549.2.dm \(\chi_{3549}(43, \cdot)\) n/a 4416 24
3549.2.dp \(\chi_{3549}(38, \cdot)\) n/a 11568 24
3549.2.dr \(\chi_{3549}(101, \cdot)\) n/a 11544 24
3549.2.dv \(\chi_{3549}(62, \cdot)\) n/a 11568 24
3549.2.dw \(\chi_{3549}(4, \cdot)\) n/a 5832 24
3549.2.dy \(\chi_{3549}(68, \cdot)\) n/a 11544 24
3549.2.eb \(\chi_{3549}(115, \cdot)\) n/a 11664 48
3549.2.ee \(\chi_{3549}(50, \cdot)\) n/a 17472 48
3549.2.ef \(\chi_{3549}(44, \cdot)\) n/a 23136 48
3549.2.ei \(\chi_{3549}(76, \cdot)\) n/a 11616 48
3549.2.ej \(\chi_{3549}(31, \cdot)\) n/a 11616 48
3549.2.el \(\chi_{3549}(11, \cdot)\) n/a 23088 48
3549.2.em \(\chi_{3549}(2, \cdot)\) n/a 23088 48
3549.2.eo \(\chi_{3549}(136, \cdot)\) n/a 11664 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3549))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3549)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)