# Properties

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

## 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

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

## 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

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