# Properties

 Label 3850.2 Level 3850 Weight 2 Dimension 125074 Nonzero newspaces 84 Sturm bound 1728000 Trace bound 19

## Defining parameters

 Level: $$N$$ = $$3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$1728000$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3850))$$.

Total New Old
Modular forms 438720 125074 313646
Cusp forms 425281 125074 300207
Eisenstein series 13439 0 13439

## Trace form

 $$125074 q - 4 q^{2} - 20 q^{3} - 8 q^{4} - 20 q^{5} - 38 q^{6} - 42 q^{7} - 4 q^{8} - 120 q^{9} + O(q^{10})$$ $$125074 q - 4 q^{2} - 20 q^{3} - 8 q^{4} - 20 q^{5} - 38 q^{6} - 42 q^{7} - 4 q^{8} - 120 q^{9} - 20 q^{10} - 56 q^{11} - 40 q^{12} - 96 q^{13} - 38 q^{14} - 80 q^{15} - 8 q^{16} - 80 q^{17} + 14 q^{18} + 6 q^{19} - 56 q^{21} + 44 q^{22} - 24 q^{23} + 42 q^{24} + 188 q^{25} + 44 q^{26} + 190 q^{27} + 94 q^{28} + 104 q^{29} + 224 q^{30} + 108 q^{31} + 6 q^{32} + 66 q^{33} + 156 q^{34} + 104 q^{35} + 102 q^{36} + 36 q^{37} + 16 q^{38} + 188 q^{39} - 20 q^{40} - 72 q^{41} + 214 q^{42} + 292 q^{43} + 142 q^{44} + 444 q^{45} + 232 q^{46} + 392 q^{47} - 20 q^{48} + 160 q^{49} + 60 q^{50} + 342 q^{51} + 204 q^{52} + 224 q^{53} + 328 q^{54} + 304 q^{55} - 28 q^{56} + 510 q^{57} + 368 q^{58} + 434 q^{59} + 160 q^{60} + 700 q^{61} + 360 q^{62} + 732 q^{63} - 8 q^{64} + 524 q^{65} + 416 q^{66} + 724 q^{67} + 300 q^{68} + 768 q^{69} + 120 q^{70} + 160 q^{71} + 4 q^{72} + 316 q^{73} + 256 q^{74} + 432 q^{75} + 76 q^{76} + 224 q^{77} + 240 q^{78} + 288 q^{79} - 20 q^{80} + 114 q^{81} + 130 q^{82} + 390 q^{83} + 84 q^{84} + 156 q^{85} + 138 q^{86} + 300 q^{87} + 52 q^{88} + 332 q^{89} + 172 q^{90} + 292 q^{91} + 68 q^{92} + 528 q^{93} + 12 q^{94} + 304 q^{95} + 68 q^{96} + 378 q^{97} + 370 q^{98} + 576 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3850))$$

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
3850.2.a $$\chi_{3850}(1, \cdot)$$ 3850.2.a.a 1 1
3850.2.a.b 1
3850.2.a.c 1
3850.2.a.d 1
3850.2.a.e 1
3850.2.a.f 1
3850.2.a.g 1
3850.2.a.h 1
3850.2.a.i 1
3850.2.a.j 1
3850.2.a.k 1
3850.2.a.l 1
3850.2.a.m 1
3850.2.a.n 1
3850.2.a.o 1
3850.2.a.p 1
3850.2.a.q 1
3850.2.a.r 1
3850.2.a.s 1
3850.2.a.t 1
3850.2.a.u 1
3850.2.a.v 1
3850.2.a.w 1
3850.2.a.x 1
3850.2.a.y 1
3850.2.a.z 1
3850.2.a.ba 1
3850.2.a.bb 1
3850.2.a.bc 2
3850.2.a.bd 2
3850.2.a.be 2
3850.2.a.bf 2
3850.2.a.bg 2
3850.2.a.bh 2
3850.2.a.bi 2
3850.2.a.bj 2
3850.2.a.bk 2
3850.2.a.bl 2
3850.2.a.bm 2
3850.2.a.bn 2
3850.2.a.bo 2
3850.2.a.bp 2
3850.2.a.bq 2
3850.2.a.br 3
3850.2.a.bs 3
3850.2.a.bt 3
3850.2.a.bu 3
3850.2.a.bv 3
3850.2.a.bw 3
3850.2.a.bx 4
3850.2.a.by 4
3850.2.a.bz 5
3850.2.a.ca 5
3850.2.c $$\chi_{3850}(1849, \cdot)$$ 3850.2.c.a 2 1
3850.2.c.b 2
3850.2.c.c 2
3850.2.c.d 2
3850.2.c.e 2
3850.2.c.f 2
3850.2.c.g 2
3850.2.c.h 2
3850.2.c.i 2
3850.2.c.j 2
3850.2.c.k 2
3850.2.c.l 2
3850.2.c.m 2
3850.2.c.n 2
3850.2.c.o 2
3850.2.c.p 2
3850.2.c.q 4
3850.2.c.r 4
3850.2.c.s 4
3850.2.c.t 4
3850.2.c.u 4
3850.2.c.v 4
3850.2.c.w 4
3850.2.c.x 4
3850.2.c.y 4
3850.2.c.z 6
3850.2.c.ba 6
3850.2.c.bb 6
3850.2.c.bc 6
3850.2.e $$\chi_{3850}(2001, \cdot)$$ n/a 152 1
3850.2.g $$\chi_{3850}(3849, \cdot)$$ n/a 144 1
3850.2.i $$\chi_{3850}(1101, \cdot)$$ n/a 256 2
3850.2.l $$\chi_{3850}(1343, \cdot)$$ n/a 240 2
3850.2.m $$\chi_{3850}(43, \cdot)$$ n/a 216 2
3850.2.n $$\chi_{3850}(771, \cdot)$$ n/a 608 4
3850.2.o $$\chi_{3850}(841, \cdot)$$ n/a 720 4
3850.2.p $$\chi_{3850}(1401, \cdot)$$ n/a 456 4
3850.2.q $$\chi_{3850}(71, \cdot)$$ n/a 720 4
3850.2.r $$\chi_{3850}(141, \cdot)$$ n/a 720 4
3850.2.s $$\chi_{3850}(1961, \cdot)$$ n/a 720 4
3850.2.t $$\chi_{3850}(549, \cdot)$$ n/a 288 2
3850.2.w $$\chi_{3850}(1299, \cdot)$$ n/a 240 2
3850.2.y $$\chi_{3850}(901, \cdot)$$ n/a 304 2
3850.2.ba $$\chi_{3850}(1709, \cdot)$$ n/a 720 4
3850.2.bc $$\chi_{3850}(321, \cdot)$$ n/a 960 4
3850.2.bj $$\chi_{3850}(2239, \cdot)$$ n/a 960 4
3850.2.bm $$\chi_{3850}(349, \cdot)$$ n/a 576 4
3850.2.bn $$\chi_{3850}(1119, \cdot)$$ n/a 960 4
3850.2.bo $$\chi_{3850}(769, \cdot)$$ n/a 960 4
3850.2.bs $$\chi_{3850}(139, \cdot)$$ n/a 960 4
3850.2.bu $$\chi_{3850}(391, \cdot)$$ n/a 960 4
3850.2.bv $$\chi_{3850}(461, \cdot)$$ n/a 960 4
3850.2.bw $$\chi_{3850}(601, \cdot)$$ n/a 608 4
3850.2.ca $$\chi_{3850}(41, \cdot)$$ n/a 960 4
3850.2.cb $$\chi_{3850}(1091, \cdot)$$ n/a 960 4
3850.2.cd $$\chi_{3850}(169, \cdot)$$ n/a 720 4
3850.2.cg $$\chi_{3850}(449, \cdot)$$ n/a 432 4
3850.2.ch $$\chi_{3850}(309, \cdot)$$ n/a 592 4
3850.2.ci $$\chi_{3850}(1989, \cdot)$$ n/a 720 4
3850.2.cm $$\chi_{3850}(379, \cdot)$$ n/a 720 4
3850.2.cn $$\chi_{3850}(629, \cdot)$$ n/a 960 4
3850.2.cq $$\chi_{3850}(243, \cdot)$$ n/a 480 4
3850.2.cr $$\chi_{3850}(1143, \cdot)$$ n/a 576 4
3850.2.cu $$\chi_{3850}(191, \cdot)$$ n/a 1920 8
3850.2.cv $$\chi_{3850}(81, \cdot)$$ n/a 1920 8
3850.2.cw $$\chi_{3850}(641, \cdot)$$ n/a 1920 8
3850.2.cx $$\chi_{3850}(401, \cdot)$$ n/a 1216 8
3850.2.cy $$\chi_{3850}(291, \cdot)$$ n/a 1920 8
3850.2.cz $$\chi_{3850}(221, \cdot)$$ n/a 1600 8
3850.2.da $$\chi_{3850}(337, \cdot)$$ n/a 1440 8
3850.2.db $$\chi_{3850}(97, \cdot)$$ n/a 1920 8
3850.2.dg $$\chi_{3850}(197, \cdot)$$ n/a 1440 8
3850.2.dh $$\chi_{3850}(127, \cdot)$$ n/a 1440 8
3850.2.di $$\chi_{3850}(57, \cdot)$$ n/a 864 8
3850.2.dj $$\chi_{3850}(673, \cdot)$$ n/a 1440 8
3850.2.dk $$\chi_{3850}(1203, \cdot)$$ n/a 1920 8
3850.2.dl $$\chi_{3850}(643, \cdot)$$ n/a 1152 8
3850.2.dm $$\chi_{3850}(27, \cdot)$$ n/a 1920 8
3850.2.dn $$\chi_{3850}(573, \cdot)$$ n/a 1600 8
3850.2.dw $$\chi_{3850}(797, \cdot)$$ n/a 1920 8
3850.2.dx $$\chi_{3850}(897, \cdot)$$ n/a 1440 8
3850.2.dz $$\chi_{3850}(369, \cdot)$$ n/a 1920 8
3850.2.ec $$\chi_{3850}(61, \cdot)$$ n/a 1920 8
3850.2.ed $$\chi_{3850}(171, \cdot)$$ n/a 1920 8
3850.2.eh $$\chi_{3850}(101, \cdot)$$ n/a 1216 8
3850.2.ei $$\chi_{3850}(131, \cdot)$$ n/a 1920 8
3850.2.ej $$\chi_{3850}(271, \cdot)$$ n/a 1920 8
3850.2.el $$\chi_{3850}(389, \cdot)$$ n/a 1920 8
3850.2.ep $$\chi_{3850}(709, \cdot)$$ n/a 1920 8
3850.2.eq $$\chi_{3850}(529, \cdot)$$ n/a 1600 8
3850.2.er $$\chi_{3850}(499, \cdot)$$ n/a 1152 8
3850.2.eu $$\chi_{3850}(9, \cdot)$$ n/a 1920 8
3850.2.fa $$\chi_{3850}(479, \cdot)$$ n/a 1920 8
3850.2.fe $$\chi_{3850}(439, \cdot)$$ n/a 1920 8
3850.2.ff $$\chi_{3850}(19, \cdot)$$ n/a 1920 8
3850.2.fg $$\chi_{3850}(299, \cdot)$$ n/a 1152 8
3850.2.fj $$\chi_{3850}(129, \cdot)$$ n/a 1920 8
3850.2.fl $$\chi_{3850}(289, \cdot)$$ n/a 1920 8
3850.2.fn $$\chi_{3850}(831, \cdot)$$ n/a 1920 8
3850.2.fo $$\chi_{3850}(383, \cdot)$$ n/a 3840 16
3850.2.fp $$\chi_{3850}(233, \cdot)$$ n/a 3840 16
3850.2.fy $$\chi_{3850}(123, \cdot)$$ n/a 3840 16
3850.2.fz $$\chi_{3850}(107, \cdot)$$ n/a 2304 16
3850.2.ga $$\chi_{3850}(387, \cdot)$$ n/a 3840 16
3850.2.gb $$\chi_{3850}(263, \cdot)$$ n/a 3840 16
3850.2.gc $$\chi_{3850}(353, \cdot)$$ n/a 3200 16
3850.2.gd $$\chi_{3850}(3, \cdot)$$ n/a 3840 16
3850.2.ge $$\chi_{3850}(157, \cdot)$$ n/a 2304 16
3850.2.gf $$\chi_{3850}(103, \cdot)$$ n/a 3840 16
3850.2.gk $$\chi_{3850}(513, \cdot)$$ n/a 3840 16
3850.2.gl $$\chi_{3850}(213, \cdot)$$ n/a 3840 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3850))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3850)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(550))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1925))$$$$^{\oplus 2}$$