## Defining parameters

 Level: $$N$$ = $$3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1622016$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3864))$$.

Total New Old
Modular forms 411840 164164 247676
Cusp forms 399169 162484 236685
Eisenstein series 12671 1680 10991

## Trace form

 $$162484 q - 8 q^{2} - 88 q^{3} - 168 q^{4} - 8 q^{5} - 68 q^{6} - 204 q^{7} + 16 q^{8} - 176 q^{9} + O(q^{10})$$ $$162484 q - 8 q^{2} - 88 q^{3} - 168 q^{4} - 8 q^{5} - 68 q^{6} - 204 q^{7} + 16 q^{8} - 176 q^{9} - 136 q^{10} - 8 q^{11} - 44 q^{12} - 32 q^{13} + 8 q^{14} - 196 q^{15} - 152 q^{16} - 32 q^{17} - 100 q^{18} - 152 q^{19} + 40 q^{20} - 304 q^{22} + 36 q^{23} - 140 q^{24} - 268 q^{25} + 88 q^{26} - 16 q^{27} - 4 q^{28} + 24 q^{29} + 4 q^{30} - 8 q^{31} + 152 q^{32} - 76 q^{33} + 72 q^{34} + 28 q^{35} - 156 q^{36} - 128 q^{37} + 104 q^{38} - 104 q^{39} - 96 q^{41} - 162 q^{42} - 584 q^{43} - 96 q^{44} + 76 q^{45} - 240 q^{46} - 128 q^{47} - 228 q^{48} - 464 q^{49} - 176 q^{50} - 80 q^{51} - 304 q^{52} - 24 q^{53} - 244 q^{54} - 216 q^{55} - 184 q^{56} - 400 q^{57} - 320 q^{58} + 72 q^{59} - 280 q^{60} - 8 q^{61} - 232 q^{62} + 18 q^{63} - 624 q^{64} + 80 q^{65} - 104 q^{66} - 8 q^{67} - 120 q^{68} - 8 q^{69} - 528 q^{70} + 128 q^{71} - 256 q^{72} - 392 q^{73} + 152 q^{74} + 4 q^{75} + 192 q^{76} - 72 q^{77} + 108 q^{78} + 64 q^{79} + 792 q^{80} + 8 q^{81} + 232 q^{82} + 152 q^{83} - 22 q^{84} + 104 q^{85} + 848 q^{86} + 116 q^{87} + 616 q^{88} + 112 q^{89} + 516 q^{90} - 104 q^{91} + 780 q^{92} - 164 q^{93} + 592 q^{94} + 256 q^{95} + 568 q^{96} + 40 q^{97} - 84 q^{98} - 64 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3864))$$

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
3864.2.a $$\chi_{3864}(1, \cdot)$$ 3864.2.a.a 1 1
3864.2.a.b 1
3864.2.a.c 1
3864.2.a.d 1
3864.2.a.e 1
3864.2.a.f 1
3864.2.a.g 2
3864.2.a.h 2
3864.2.a.i 2
3864.2.a.j 2
3864.2.a.k 3
3864.2.a.l 3
3864.2.a.m 3
3864.2.a.n 3
3864.2.a.o 3
3864.2.a.p 3
3864.2.a.q 3
3864.2.a.r 4
3864.2.a.s 4
3864.2.a.t 4
3864.2.a.u 4
3864.2.a.v 5
3864.2.a.w 6
3864.2.a.x 6
3864.2.b $$\chi_{3864}(3863, \cdot)$$ None 0 1
3864.2.c $$\chi_{3864}(2071, \cdot)$$ None 0 1
3864.2.d $$\chi_{3864}(1933, \cdot)$$ n/a 264 1
3864.2.e $$\chi_{3864}(3725, \cdot)$$ n/a 576 1
3864.2.n $$\chi_{3864}(2255, \cdot)$$ None 0 1
3864.2.o $$\chi_{3864}(1471, \cdot)$$ None 0 1
3864.2.p $$\chi_{3864}(3541, \cdot)$$ n/a 384 1
3864.2.q $$\chi_{3864}(461, \cdot)$$ n/a 704 1
3864.2.r $$\chi_{3864}(3403, \cdot)$$ n/a 288 1
3864.2.s $$\chi_{3864}(323, \cdot)$$ n/a 528 1
3864.2.t $$\chi_{3864}(2393, \cdot)$$ n/a 176 1
3864.2.u $$\chi_{3864}(1609, \cdot)$$ 3864.2.u.a 4 1
3864.2.u.b 4
3864.2.u.c 8
3864.2.u.d 8
3864.2.u.e 8
3864.2.u.f 16
3864.2.u.g 16
3864.2.u.h 32
3864.2.bd $$\chi_{3864}(139, \cdot)$$ n/a 352 1
3864.2.be $$\chi_{3864}(1931, \cdot)$$ n/a 760 1
3864.2.bf $$\chi_{3864}(1793, \cdot)$$ n/a 144 1
3864.2.bg $$\chi_{3864}(2209, \cdot)$$ n/a 176 2
3864.2.bl $$\chi_{3864}(137, \cdot)$$ n/a 384 2
3864.2.bm $$\chi_{3864}(2483, \cdot)$$ n/a 1520 2
3864.2.bn $$\chi_{3864}(691, \cdot)$$ n/a 704 2
3864.2.bo $$\chi_{3864}(2161, \cdot)$$ n/a 192 2
3864.2.bp $$\chi_{3864}(185, \cdot)$$ n/a 352 2
3864.2.bq $$\chi_{3864}(2531, \cdot)$$ n/a 1408 2
3864.2.br $$\chi_{3864}(1747, \cdot)$$ n/a 768 2
3864.2.ca $$\chi_{3864}(1013, \cdot)$$ n/a 1408 2
3864.2.cb $$\chi_{3864}(229, \cdot)$$ n/a 768 2
3864.2.cc $$\chi_{3864}(919, \cdot)$$ None 0 2
3864.2.cd $$\chi_{3864}(599, \cdot)$$ None 0 2
3864.2.ce $$\chi_{3864}(2069, \cdot)$$ n/a 1520 2
3864.2.cf $$\chi_{3864}(277, \cdot)$$ n/a 704 2
3864.2.cg $$\chi_{3864}(2623, \cdot)$$ None 0 2
3864.2.ch $$\chi_{3864}(551, \cdot)$$ None 0 2
3864.2.cm $$\chi_{3864}(169, \cdot)$$ n/a 720 10
3864.2.cn $$\chi_{3864}(113, \cdot)$$ n/a 1440 10
3864.2.co $$\chi_{3864}(83, \cdot)$$ n/a 7600 10
3864.2.cp $$\chi_{3864}(307, \cdot)$$ n/a 3840 10
3864.2.cy $$\chi_{3864}(97, \cdot)$$ n/a 960 10
3864.2.cz $$\chi_{3864}(41, \cdot)$$ n/a 1920 10
3864.2.da $$\chi_{3864}(491, \cdot)$$ n/a 5760 10
3864.2.db $$\chi_{3864}(43, \cdot)$$ n/a 2880 10
3864.2.dc $$\chi_{3864}(629, \cdot)$$ n/a 7600 10
3864.2.dd $$\chi_{3864}(181, \cdot)$$ n/a 3840 10
3864.2.de $$\chi_{3864}(295, \cdot)$$ None 0 10
3864.2.df $$\chi_{3864}(71, \cdot)$$ None 0 10
3864.2.do $$\chi_{3864}(365, \cdot)$$ n/a 5760 10
3864.2.dp $$\chi_{3864}(85, \cdot)$$ n/a 2880 10
3864.2.dq $$\chi_{3864}(55, \cdot)$$ None 0 10
3864.2.dr $$\chi_{3864}(503, \cdot)$$ None 0 10
3864.2.ds $$\chi_{3864}(25, \cdot)$$ n/a 1920 20
3864.2.dx $$\chi_{3864}(143, \cdot)$$ None 0 20
3864.2.dy $$\chi_{3864}(31, \cdot)$$ None 0 20
3864.2.dz $$\chi_{3864}(445, \cdot)$$ n/a 7680 20
3864.2.ea $$\chi_{3864}(53, \cdot)$$ n/a 15200 20
3864.2.eb $$\chi_{3864}(95, \cdot)$$ None 0 20
3864.2.ec $$\chi_{3864}(79, \cdot)$$ None 0 20
3864.2.ed $$\chi_{3864}(61, \cdot)$$ n/a 7680 20
3864.2.ee $$\chi_{3864}(101, \cdot)$$ n/a 15200 20
3864.2.en $$\chi_{3864}(67, \cdot)$$ n/a 7680 20
3864.2.eo $$\chi_{3864}(179, \cdot)$$ n/a 15200 20
3864.2.ep $$\chi_{3864}(257, \cdot)$$ n/a 3840 20
3864.2.eq $$\chi_{3864}(145, \cdot)$$ n/a 1920 20
3864.2.er $$\chi_{3864}(187, \cdot)$$ n/a 7680 20
3864.2.es $$\chi_{3864}(227, \cdot)$$ n/a 15200 20
3864.2.et $$\chi_{3864}(65, \cdot)$$ n/a 3840 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3864))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3864)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(552))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1288))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1932))$$$$^{\oplus 2}$$