# Properties

 Label 3800.2 Level 3800 Weight 2 Dimension 221327 Nonzero newspaces 54 Sturm bound 1728000 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$54$$ Sturm bound: $$1728000$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3800))$$.

Total New Old
Modular forms 438048 224115 213933
Cusp forms 425953 221327 204626
Eisenstein series 12095 2788 9307

## Trace form

 $$221327 q - 210 q^{2} - 210 q^{3} - 210 q^{4} - 2 q^{5} - 338 q^{6} - 226 q^{7} - 210 q^{8} - 440 q^{9} + O(q^{10})$$ $$221327 q - 210 q^{2} - 210 q^{3} - 210 q^{4} - 2 q^{5} - 338 q^{6} - 226 q^{7} - 210 q^{8} - 440 q^{9} - 256 q^{10} - 354 q^{11} - 162 q^{12} - 8 q^{13} - 162 q^{14} - 240 q^{15} - 274 q^{16} - 412 q^{17} - 98 q^{18} - 190 q^{19} - 504 q^{20} + 32 q^{21} - 130 q^{22} - 194 q^{23} - 98 q^{24} - 522 q^{25} - 594 q^{26} - 171 q^{27} - 226 q^{28} - 42 q^{29} - 248 q^{30} - 324 q^{31} - 290 q^{32} - 474 q^{33} - 338 q^{34} - 232 q^{35} - 466 q^{36} + 16 q^{37} - 262 q^{38} - 370 q^{39} - 336 q^{40} - 662 q^{41} - 290 q^{42} - 70 q^{43} - 258 q^{44} + 158 q^{45} - 434 q^{46} - 36 q^{47} - 226 q^{48} - 288 q^{49} - 216 q^{50} - 483 q^{51} - 114 q^{52} + 114 q^{53} - 44 q^{54} - 112 q^{55} - 114 q^{56} - 316 q^{57} - 252 q^{58} - 34 q^{59} - 168 q^{60} - 30 q^{61} + 120 q^{62} - 74 q^{63} + 78 q^{64} - 458 q^{65} - 98 q^{66} - 166 q^{67} + 12 q^{68} + 32 q^{69} - 248 q^{70} - 348 q^{71} - 92 q^{72} - 203 q^{73} - 130 q^{74} - 400 q^{75} - 566 q^{76} - 10 q^{77} - 270 q^{78} - 388 q^{79} - 296 q^{80} - 519 q^{81} - 228 q^{82} - 500 q^{83} - 426 q^{84} - 146 q^{85} - 388 q^{86} - 518 q^{87} - 530 q^{88} - 308 q^{89} - 856 q^{90} - 538 q^{91} - 568 q^{92} - 222 q^{93} - 670 q^{94} - 400 q^{95} - 892 q^{96} - 600 q^{97} - 706 q^{98} - 673 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3800))$$

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
3800.2.a $$\chi_{3800}(1, \cdot)$$ 3800.2.a.a 1 1
3800.2.a.b 1
3800.2.a.c 1
3800.2.a.d 1
3800.2.a.e 1
3800.2.a.f 1
3800.2.a.g 1
3800.2.a.h 1
3800.2.a.i 1
3800.2.a.j 2
3800.2.a.k 2
3800.2.a.l 2
3800.2.a.m 2
3800.2.a.n 2
3800.2.a.o 2
3800.2.a.p 2
3800.2.a.q 2
3800.2.a.r 3
3800.2.a.s 3
3800.2.a.t 3
3800.2.a.u 3
3800.2.a.v 3
3800.2.a.w 3
3800.2.a.x 3
3800.2.a.y 3
3800.2.a.z 6
3800.2.a.ba 6
3800.2.a.bb 6
3800.2.a.bc 6
3800.2.a.bd 6
3800.2.a.be 6
3800.2.d $$\chi_{3800}(3649, \cdot)$$ 3800.2.d.a 2 1
3800.2.d.b 2
3800.2.d.c 2
3800.2.d.d 2
3800.2.d.e 2
3800.2.d.f 2
3800.2.d.g 2
3800.2.d.h 4
3800.2.d.i 4
3800.2.d.j 6
3800.2.d.k 6
3800.2.d.l 6
3800.2.d.m 6
3800.2.d.n 6
3800.2.d.o 6
3800.2.d.p 12
3800.2.d.q 12
3800.2.e $$\chi_{3800}(2051, \cdot)$$ n/a 374 1
3800.2.f $$\chi_{3800}(1901, \cdot)$$ n/a 342 1
3800.2.g $$\chi_{3800}(3799, \cdot)$$ None 0 1
3800.2.j $$\chi_{3800}(151, \cdot)$$ None 0 1
3800.2.k $$\chi_{3800}(1749, \cdot)$$ n/a 324 1
3800.2.p $$\chi_{3800}(1899, \cdot)$$ n/a 356 1
3800.2.q $$\chi_{3800}(201, \cdot)$$ n/a 190 2
3800.2.t $$\chi_{3800}(493, \cdot)$$ n/a 712 2
3800.2.u $$\chi_{3800}(343, \cdot)$$ None 0 2
3800.2.v $$\chi_{3800}(2393, \cdot)$$ n/a 180 2
3800.2.w $$\chi_{3800}(2243, \cdot)$$ n/a 648 2
3800.2.z $$\chi_{3800}(761, \cdot)$$ n/a 544 4
3800.2.ba $$\chi_{3800}(349, \cdot)$$ n/a 712 2
3800.2.bb $$\chi_{3800}(1551, \cdot)$$ None 0 2
3800.2.bg $$\chi_{3800}(1699, \cdot)$$ n/a 712 2
3800.2.bj $$\chi_{3800}(1851, \cdot)$$ n/a 748 2
3800.2.bk $$\chi_{3800}(49, \cdot)$$ n/a 180 2
3800.2.bl $$\chi_{3800}(1399, \cdot)$$ None 0 2
3800.2.bm $$\chi_{3800}(501, \cdot)$$ n/a 748 2
3800.2.bp $$\chi_{3800}(1201, \cdot)$$ n/a 570 6
3800.2.bs $$\chi_{3800}(229, \cdot)$$ n/a 2160 4
3800.2.bt $$\chi_{3800}(911, \cdot)$$ None 0 4
3800.2.bu $$\chi_{3800}(379, \cdot)$$ n/a 2384 4
3800.2.bx $$\chi_{3800}(531, \cdot)$$ n/a 2384 4
3800.2.by $$\chi_{3800}(609, \cdot)$$ n/a 536 4
3800.2.cd $$\chi_{3800}(759, \cdot)$$ None 0 4
3800.2.ce $$\chi_{3800}(381, \cdot)$$ n/a 2160 4
3800.2.cf $$\chi_{3800}(293, \cdot)$$ n/a 1424 4
3800.2.cg $$\chi_{3800}(7, \cdot)$$ None 0 4
3800.2.cl $$\chi_{3800}(1057, \cdot)$$ n/a 360 4
3800.2.cm $$\chi_{3800}(843, \cdot)$$ n/a 1424 4
3800.2.cn $$\chi_{3800}(121, \cdot)$$ n/a 1200 8
3800.2.co $$\chi_{3800}(299, \cdot)$$ n/a 2136 6
3800.2.ct $$\chi_{3800}(101, \cdot)$$ n/a 2244 6
3800.2.cu $$\chi_{3800}(599, \cdot)$$ None 0 6
3800.2.cx $$\chi_{3800}(1049, \cdot)$$ n/a 540 6
3800.2.cy $$\chi_{3800}(51, \cdot)$$ n/a 2244 6
3800.2.cz $$\chi_{3800}(751, \cdot)$$ None 0 6
3800.2.da $$\chi_{3800}(149, \cdot)$$ n/a 2136 6
3800.2.df $$\chi_{3800}(267, \cdot)$$ n/a 4320 8
3800.2.dg $$\chi_{3800}(113, \cdot)$$ n/a 1200 8
3800.2.dh $$\chi_{3800}(647, \cdot)$$ None 0 8
3800.2.di $$\chi_{3800}(37, \cdot)$$ n/a 4768 8
3800.2.dl $$\chi_{3800}(729, \cdot)$$ n/a 1200 8
3800.2.dm $$\chi_{3800}(331, \cdot)$$ n/a 4768 8
3800.2.dr $$\chi_{3800}(581, \cdot)$$ n/a 4768 8
3800.2.ds $$\chi_{3800}(559, \cdot)$$ None 0 8
3800.2.dv $$\chi_{3800}(31, \cdot)$$ None 0 8
3800.2.dw $$\chi_{3800}(429, \cdot)$$ n/a 4768 8
3800.2.dx $$\chi_{3800}(179, \cdot)$$ n/a 4768 8
3800.2.ec $$\chi_{3800}(193, \cdot)$$ n/a 1080 12
3800.2.ed $$\chi_{3800}(43, \cdot)$$ n/a 4272 12
3800.2.eg $$\chi_{3800}(357, \cdot)$$ n/a 4272 12
3800.2.eh $$\chi_{3800}(207, \cdot)$$ None 0 12
3800.2.ei $$\chi_{3800}(81, \cdot)$$ n/a 3600 24
3800.2.ej $$\chi_{3800}(83, \cdot)$$ n/a 9536 16
3800.2.ek $$\chi_{3800}(217, \cdot)$$ n/a 2400 16
3800.2.ep $$\chi_{3800}(87, \cdot)$$ None 0 16
3800.2.eq $$\chi_{3800}(373, \cdot)$$ n/a 9536 16
3800.2.er $$\chi_{3800}(79, \cdot)$$ None 0 24
3800.2.es $$\chi_{3800}(61, \cdot)$$ n/a 14304 24
3800.2.ex $$\chi_{3800}(59, \cdot)$$ n/a 14304 24
3800.2.fa $$\chi_{3800}(309, \cdot)$$ n/a 14304 24
3800.2.fb $$\chi_{3800}(71, \cdot)$$ None 0 24
3800.2.fc $$\chi_{3800}(91, \cdot)$$ n/a 14304 24
3800.2.fd $$\chi_{3800}(9, \cdot)$$ n/a 3600 24
3800.2.fg $$\chi_{3800}(23, \cdot)$$ None 0 48
3800.2.fh $$\chi_{3800}(13, \cdot)$$ n/a 28608 48
3800.2.fk $$\chi_{3800}(123, \cdot)$$ n/a 28608 48
3800.2.fl $$\chi_{3800}(33, \cdot)$$ n/a 7200 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3800))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3800)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1900))$$$$^{\oplus 2}$$