# Properties

 Label 3724.2 Level 3724 Weight 2 Dimension 234019 Nonzero newspaces 64 Sturm bound 1693440 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$3724 = 2^{2} \cdot 7^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$1693440$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3724))$$.

Total New Old
Modular forms 428760 237319 191441
Cusp forms 417961 234019 183942
Eisenstein series 10799 3300 7499

## Trace form

 $$234019 q - 249 q^{2} - 4 q^{3} - 249 q^{4} - 510 q^{5} - 237 q^{6} - 8 q^{7} - 429 q^{8} - 490 q^{9} + O(q^{10})$$ $$234019 q - 249 q^{2} - 4 q^{3} - 249 q^{4} - 510 q^{5} - 237 q^{6} - 8 q^{7} - 429 q^{8} - 490 q^{9} - 213 q^{10} + 12 q^{11} - 189 q^{12} - 470 q^{13} - 264 q^{14} + 6 q^{15} - 201 q^{16} - 519 q^{17} - 216 q^{18} - 19 q^{19} - 516 q^{20} - 554 q^{21} - 489 q^{22} - 21 q^{23} - 285 q^{24} - 484 q^{25} - 285 q^{26} - 43 q^{27} - 336 q^{28} - 816 q^{29} - 198 q^{30} + 46 q^{31} - 204 q^{32} - 384 q^{33} - 192 q^{34} + 30 q^{35} - 291 q^{36} - 354 q^{37} - 159 q^{38} + 144 q^{39} - 126 q^{40} - 324 q^{41} - 258 q^{42} + 85 q^{43} - 120 q^{44} - 213 q^{45} - 144 q^{46} + 111 q^{47} - 216 q^{48} - 428 q^{49} - 714 q^{50} + 120 q^{51} - 237 q^{52} - 510 q^{53} - 336 q^{54} + 102 q^{55} - 264 q^{56} - 991 q^{57} - 540 q^{58} + 3 q^{59} - 276 q^{60} - 438 q^{61} - 282 q^{62} + 36 q^{63} - 453 q^{64} - 441 q^{65} - 333 q^{66} + 43 q^{67} - 300 q^{68} - 333 q^{69} - 270 q^{70} - 9 q^{71} - 432 q^{72} - 272 q^{73} - 339 q^{74} + 26 q^{75} - 348 q^{76} - 1170 q^{77} - 609 q^{78} + 76 q^{79} - 531 q^{80} - 457 q^{81} - 534 q^{82} - 81 q^{83} - 744 q^{84} - 774 q^{85} - 666 q^{86} - 348 q^{87} - 699 q^{88} - 459 q^{89} - 1062 q^{90} - 184 q^{91} - 780 q^{92} - 956 q^{93} - 726 q^{94} - 153 q^{95} - 1254 q^{96} - 797 q^{97} - 900 q^{98} - 297 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3724))$$

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
3724.2.a $$\chi_{3724}(1, \cdot)$$ 3724.2.a.a 1 1
3724.2.a.b 1
3724.2.a.c 2
3724.2.a.d 2
3724.2.a.e 2
3724.2.a.f 2
3724.2.a.g 2
3724.2.a.h 3
3724.2.a.i 3
3724.2.a.j 3
3724.2.a.k 5
3724.2.a.l 5
3724.2.a.m 7
3724.2.a.n 7
3724.2.a.o 8
3724.2.a.p 8
3724.2.f $$\chi_{3724}(2547, \cdot)$$ n/a 360 1
3724.2.g $$\chi_{3724}(1861, \cdot)$$ 3724.2.g.a 2 1
3724.2.g.b 2
3724.2.g.c 4
3724.2.g.d 4
3724.2.g.e 8
3724.2.g.f 16
3724.2.g.g 32
3724.2.h $$\chi_{3724}(3039, \cdot)$$ n/a 400 1
3724.2.i $$\chi_{3724}(3117, \cdot)$$ n/a 120 2
3724.2.j $$\chi_{3724}(197, \cdot)$$ n/a 138 2
3724.2.k $$\chi_{3724}(1341, \cdot)$$ n/a 132 2
3724.2.l $$\chi_{3724}(961, \cdot)$$ n/a 132 2
3724.2.q $$\chi_{3724}(521, \cdot)$$ n/a 132 2
3724.2.r $$\chi_{3724}(619, \cdot)$$ n/a 784 2
3724.2.s $$\chi_{3724}(1471, \cdot)$$ n/a 800 2
3724.2.t $$\chi_{3724}(2431, \cdot)$$ n/a 784 2
3724.2.u $$\chi_{3724}(391, \cdot)$$ n/a 784 2
3724.2.v $$\chi_{3724}(2089, \cdot)$$ n/a 132 2
3724.2.w $$\chi_{3724}(2775, \cdot)$$ n/a 720 2
3724.2.x $$\chi_{3724}(293, \cdot)$$ n/a 136 2
3724.2.y $$\chi_{3724}(1243, \cdot)$$ n/a 784 2
3724.2.bl $$\chi_{3724}(863, \cdot)$$ n/a 784 2
3724.2.bm $$\chi_{3724}(901, \cdot)$$ n/a 132 2
3724.2.bn $$\chi_{3724}(999, \cdot)$$ n/a 784 2
3724.2.bo $$\chi_{3724}(533, \cdot)$$ n/a 504 6
3724.2.bp $$\chi_{3724}(785, \cdot)$$ n/a 408 6
3724.2.bq $$\chi_{3724}(177, \cdot)$$ n/a 402 6
3724.2.br $$\chi_{3724}(557, \cdot)$$ n/a 402 6
3724.2.bs $$\chi_{3724}(379, \cdot)$$ n/a 3336 6
3724.2.bt $$\chi_{3724}(265, \cdot)$$ n/a 552 6
3724.2.bu $$\chi_{3724}(419, \cdot)$$ n/a 3024 6
3724.2.bz $$\chi_{3724}(803, \cdot)$$ n/a 2352 6
3724.2.ca $$\chi_{3724}(67, \cdot)$$ n/a 2352 6
3724.2.cd $$\chi_{3724}(97, \cdot)$$ n/a 396 6
3724.2.ce $$\chi_{3724}(325, \cdot)$$ n/a 402 6
3724.2.cj $$\chi_{3724}(295, \cdot)$$ n/a 2400 6
3724.2.ck $$\chi_{3724}(195, \cdot)$$ n/a 2352 6
3724.2.cl $$\chi_{3724}(215, \cdot)$$ n/a 2352 6
3724.2.cm $$\chi_{3724}(459, \cdot)$$ n/a 2352 6
3724.2.cr $$\chi_{3724}(117, \cdot)$$ n/a 402 6
3724.2.cu $$\chi_{3724}(429, \cdot)$$ n/a 1128 12
3724.2.cv $$\chi_{3724}(121, \cdot)$$ n/a 1128 12
3724.2.cw $$\chi_{3724}(505, \cdot)$$ n/a 1104 12
3724.2.cx $$\chi_{3724}(305, \cdot)$$ n/a 1008 12
3724.2.cy $$\chi_{3724}(311, \cdot)$$ n/a 6672 12
3724.2.cz $$\chi_{3724}(297, \cdot)$$ n/a 1128 12
3724.2.da $$\chi_{3724}(331, \cdot)$$ n/a 6672 12
3724.2.dn $$\chi_{3724}(107, \cdot)$$ n/a 6672 12
3724.2.do $$\chi_{3724}(69, \cdot)$$ n/a 1104 12
3724.2.dp $$\chi_{3724}(115, \cdot)$$ n/a 6048 12
3724.2.dq $$\chi_{3724}(341, \cdot)$$ n/a 1128 12
3724.2.dr $$\chi_{3724}(83, \cdot)$$ n/a 6672 12
3724.2.ds $$\chi_{3724}(151, \cdot)$$ n/a 6672 12
3724.2.dt $$\chi_{3724}(183, \cdot)$$ n/a 6672 12
3724.2.du $$\chi_{3724}(87, \cdot)$$ n/a 6672 12
3724.2.dv $$\chi_{3724}(145, \cdot)$$ n/a 1128 12
3724.2.ea $$\chi_{3724}(25, \cdot)$$ n/a 3348 36
3724.2.eb $$\chi_{3724}(85, \cdot)$$ n/a 3384 36
3724.2.ec $$\chi_{3724}(9, \cdot)$$ n/a 3348 36
3724.2.ef $$\chi_{3724}(33, \cdot)$$ n/a 3348 36
3724.2.ek $$\chi_{3724}(55, \cdot)$$ n/a 20016 36
3724.2.el $$\chi_{3724}(15, \cdot)$$ n/a 20016 36
3724.2.em $$\chi_{3724}(51, \cdot)$$ n/a 20016 36
3724.2.en $$\chi_{3724}(47, \cdot)$$ n/a 20016 36
3724.2.es $$\chi_{3724}(13, \cdot)$$ n/a 3384 36
3724.2.et $$\chi_{3724}(89, \cdot)$$ n/a 3348 36
3724.2.ew $$\chi_{3724}(135, \cdot)$$ n/a 20016 36
3724.2.ex $$\chi_{3724}(131, \cdot)$$ n/a 20016 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3724))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3724)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1862))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3724))$$$$^{\oplus 1}$$