# Properties

 Label 3822.2 Level 3822 Weight 2 Dimension 93668 Nonzero newspaces 60 Sturm bound 1580544 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$1580544$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3822))$$.

Total New Old
Modular forms 400896 93668 307228
Cusp forms 389377 93668 295709
Eisenstein series 11519 0 11519

## Trace form

 $$93668 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 22 q^{6} - 32 q^{7} - 4 q^{8} - 34 q^{9} + O(q^{10})$$ $$93668 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 22 q^{6} - 32 q^{7} - 4 q^{8} - 34 q^{9} - 66 q^{10} - 96 q^{11} - 10 q^{12} - 66 q^{13} - 12 q^{15} - 6 q^{16} - 42 q^{17} + 44 q^{18} - 80 q^{19} + 6 q^{20} + 20 q^{21} + 24 q^{22} - 24 q^{23} + 26 q^{24} - 64 q^{25} - 10 q^{26} - 42 q^{27} - 24 q^{28} - 66 q^{29} - 12 q^{30} - 120 q^{31} + 2 q^{32} - 60 q^{33} - 60 q^{34} - 96 q^{35} - 6 q^{36} + 70 q^{37} + 64 q^{38} + 100 q^{39} + 132 q^{40} + 222 q^{41} + 108 q^{42} + 72 q^{43} + 96 q^{44} + 186 q^{45} + 360 q^{46} + 264 q^{47} + 22 q^{48} + 576 q^{49} + 200 q^{50} + 396 q^{51} + 52 q^{52} + 228 q^{53} + 38 q^{54} + 720 q^{55} + 144 q^{56} + 32 q^{57} + 390 q^{58} + 168 q^{59} + 120 q^{60} + 278 q^{61} + 64 q^{62} + 60 q^{63} - 20 q^{64} - 186 q^{65} - 24 q^{66} - 64 q^{67} - 18 q^{68} - 96 q^{69} - 192 q^{71} - 70 q^{72} - 44 q^{73} + 142 q^{74} + 218 q^{75} + 304 q^{76} + 216 q^{77} + 194 q^{78} + 688 q^{79} - 42 q^{80} + 14 q^{81} + 846 q^{82} + 816 q^{83} + 116 q^{84} + 1362 q^{85} + 376 q^{86} + 996 q^{87} - 24 q^{88} + 1164 q^{89} + 228 q^{90} + 680 q^{91} + 480 q^{92} + 1040 q^{93} + 1128 q^{94} + 1536 q^{95} + 26 q^{96} + 1716 q^{97} + 240 q^{98} + 396 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3822))$$

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
3822.2.a $$\chi_{3822}(1, \cdot)$$ 3822.2.a.a 1 1
3822.2.a.b 1
3822.2.a.c 1
3822.2.a.d 1
3822.2.a.e 1
3822.2.a.f 1
3822.2.a.g 1
3822.2.a.h 1
3822.2.a.i 1
3822.2.a.j 1
3822.2.a.k 1
3822.2.a.l 1
3822.2.a.m 1
3822.2.a.n 1
3822.2.a.o 1
3822.2.a.p 1
3822.2.a.q 1
3822.2.a.r 1
3822.2.a.s 1
3822.2.a.t 1
3822.2.a.u 1
3822.2.a.v 1
3822.2.a.w 1
3822.2.a.x 1
3822.2.a.y 1
3822.2.a.z 1
3822.2.a.ba 1
3822.2.a.bb 1
3822.2.a.bc 1
3822.2.a.bd 1
3822.2.a.be 1
3822.2.a.bf 1
3822.2.a.bg 1
3822.2.a.bh 1
3822.2.a.bi 2
3822.2.a.bj 2
3822.2.a.bk 2
3822.2.a.bl 2
3822.2.a.bm 2
3822.2.a.bn 2
3822.2.a.bo 2
3822.2.a.bp 2
3822.2.a.bq 2
3822.2.a.br 2
3822.2.a.bs 2
3822.2.a.bt 2
3822.2.a.bu 2
3822.2.a.bv 3
3822.2.a.bw 3
3822.2.a.bx 4
3822.2.a.by 4
3822.2.a.bz 4
3822.2.a.ca 4
3822.2.c $$\chi_{3822}(883, \cdot)$$ 3822.2.c.a 2 1
3822.2.c.b 2
3822.2.c.c 2
3822.2.c.d 2
3822.2.c.e 2
3822.2.c.f 4
3822.2.c.g 4
3822.2.c.h 4
3822.2.c.i 6
3822.2.c.j 6
3822.2.c.k 6
3822.2.c.l 6
3822.2.c.m 10
3822.2.c.n 10
3822.2.c.o 16
3822.2.c.p 16
3822.2.e $$\chi_{3822}(3821, \cdot)$$ n/a 184 1
3822.2.g $$\chi_{3822}(2939, \cdot)$$ n/a 160 1
3822.2.i $$\chi_{3822}(79, \cdot)$$ n/a 160 2
3822.2.j $$\chi_{3822}(2713, \cdot)$$ n/a 188 2
3822.2.k $$\chi_{3822}(373, \cdot)$$ n/a 188 2
3822.2.l $$\chi_{3822}(295, \cdot)$$ n/a 188 2
3822.2.o $$\chi_{3822}(2449, \cdot)$$ n/a 192 2
3822.2.p $$\chi_{3822}(785, \cdot)$$ n/a 380 2
3822.2.q $$\chi_{3822}(881, \cdot)$$ n/a 376 2
3822.2.s $$\chi_{3822}(589, \cdot)$$ n/a 192 2
3822.2.u $$\chi_{3822}(3155, \cdot)$$ n/a 372 2
3822.2.z $$\chi_{3822}(521, \cdot)$$ n/a 320 2
3822.2.bb $$\chi_{3822}(815, \cdot)$$ n/a 372 2
3822.2.bd $$\chi_{3822}(361, \cdot)$$ n/a 188 2
3822.2.bg $$\chi_{3822}(1403, \cdot)$$ n/a 376 2
3822.2.bi $$\chi_{3822}(803, \cdot)$$ n/a 372 2
3822.2.bk $$\chi_{3822}(961, \cdot)$$ n/a 184 2
3822.2.bm $$\chi_{3822}(1843, \cdot)$$ n/a 188 2
3822.2.bn $$\chi_{3822}(2285, \cdot)$$ n/a 372 2
3822.2.bq $$\chi_{3822}(2057, \cdot)$$ n/a 376 2
3822.2.bs $$\chi_{3822}(547, \cdot)$$ n/a 672 6
3822.2.bv $$\chi_{3822}(197, \cdot)$$ n/a 768 4
3822.2.bw $$\chi_{3822}(863, \cdot)$$ n/a 752 4
3822.2.bx $$\chi_{3822}(557, \cdot)$$ n/a 744 4
3822.2.by $$\chi_{3822}(97, \cdot)$$ n/a 368 4
3822.2.bz $$\chi_{3822}(19, \cdot)$$ n/a 376 4
3822.2.ca $$\chi_{3822}(31, \cdot)$$ n/a 368 4
3822.2.ch $$\chi_{3822}(1501, \cdot)$$ n/a 376 4
3822.2.ci $$\chi_{3822}(275, \cdot)$$ n/a 744 4
3822.2.ck $$\chi_{3822}(209, \cdot)$$ n/a 1344 6
3822.2.cm $$\chi_{3822}(545, \cdot)$$ n/a 1584 6
3822.2.co $$\chi_{3822}(337, \cdot)$$ n/a 768 6
3822.2.cq $$\chi_{3822}(211, \cdot)$$ n/a 1584 12
3822.2.cr $$\chi_{3822}(445, \cdot)$$ n/a 1560 12
3822.2.cs $$\chi_{3822}(289, \cdot)$$ n/a 1560 12
3822.2.ct $$\chi_{3822}(235, \cdot)$$ n/a 1344 12
3822.2.cu $$\chi_{3822}(239, \cdot)$$ n/a 3168 12
3822.2.cv $$\chi_{3822}(265, \cdot)$$ n/a 1536 12
3822.2.cz $$\chi_{3822}(419, \cdot)$$ n/a 3120 12
3822.2.dc $$\chi_{3822}(101, \cdot)$$ n/a 3144 12
3822.2.dd $$\chi_{3822}(205, \cdot)$$ n/a 1560 12
3822.2.df $$\chi_{3822}(25, \cdot)$$ n/a 1584 12
3822.2.dh $$\chi_{3822}(17, \cdot)$$ n/a 3144 12
3822.2.dj $$\chi_{3822}(311, \cdot)$$ n/a 3120 12
3822.2.dm $$\chi_{3822}(121, \cdot)$$ n/a 1560 12
3822.2.do $$\chi_{3822}(269, \cdot)$$ n/a 3144 12
3822.2.dq $$\chi_{3822}(131, \cdot)$$ n/a 2688 12
3822.2.dv $$\chi_{3822}(185, \cdot)$$ n/a 3144 12
3822.2.dx $$\chi_{3822}(43, \cdot)$$ n/a 1584 12
3822.2.dz $$\chi_{3822}(251, \cdot)$$ n/a 3120 12
3822.2.ea $$\chi_{3822}(137, \cdot)$$ n/a 6288 24
3822.2.eb $$\chi_{3822}(145, \cdot)$$ n/a 3120 24
3822.2.ei $$\chi_{3822}(73, \cdot)$$ n/a 3168 24
3822.2.ej $$\chi_{3822}(115, \cdot)$$ n/a 3120 24
3822.2.ek $$\chi_{3822}(223, \cdot)$$ n/a 3168 24
3822.2.el $$\chi_{3822}(11, \cdot)$$ n/a 6288 24
3822.2.em $$\chi_{3822}(317, \cdot)$$ n/a 6240 24
3822.2.en $$\chi_{3822}(71, \cdot)$$ n/a 6240 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3822))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3822)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1274))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1911))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3822))$$$$^{\oplus 1}$$