## Defining parameters

 Level: $$N$$ = $$1862 = 2 \cdot 7^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$423360$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1862))$$.

Total New Old
Modular forms 108000 33665 74335
Cusp forms 103681 33665 70016
Eisenstein series 4319 0 4319

## Trace form

 $$33665 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + O(q^{10})$$ $$33665 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + 12 q^{10} + 24 q^{11} + 6 q^{12} + 36 q^{13} + 12 q^{14} + 84 q^{15} + 6 q^{16} + 78 q^{17} + 49 q^{18} + 66 q^{19} + 30 q^{20} + 52 q^{21} + 51 q^{22} + 66 q^{23} + 16 q^{24} + 78 q^{25} + 62 q^{26} + 129 q^{27} + 16 q^{28} + 54 q^{29} + 48 q^{30} + 66 q^{31} - 2 q^{32} + 150 q^{33} + 12 q^{34} + 84 q^{35} + 30 q^{36} - 10 q^{37} - 26 q^{38} + 2 q^{39} - 72 q^{40} - 42 q^{41} - 108 q^{42} - 6 q^{43} - 51 q^{44} - 156 q^{45} - 168 q^{46} - 48 q^{47} - 19 q^{48} - 236 q^{49} - 14 q^{50} - 141 q^{51} - 10 q^{52} + 36 q^{53} - 134 q^{54} - 204 q^{55} - 72 q^{56} + 78 q^{57} - 48 q^{58} + 18 q^{59} + 38 q^{61} + 50 q^{62} + 72 q^{63} + 12 q^{64} + 276 q^{65} + 168 q^{66} + 198 q^{67} + 69 q^{68} + 246 q^{69} + 84 q^{70} + 216 q^{71} + 31 q^{72} + 189 q^{73} + 68 q^{74} + 330 q^{75} + 24 q^{76} + 168 q^{77} + 116 q^{78} + 270 q^{79} + 12 q^{80} + 129 q^{81} + 96 q^{82} + 48 q^{83} + 52 q^{84} + 120 q^{85} + 92 q^{86} + 132 q^{87} + 24 q^{88} + 60 q^{89} + 246 q^{90} + 20 q^{91} + 84 q^{92} - 66 q^{93} + 216 q^{94} + 42 q^{95} + 16 q^{96} + 78 q^{97} + 96 q^{98} + 183 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1862))$$

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
1862.2.a $$\chi_{1862}(1, \cdot)$$ 1862.2.a.a 1 1
1862.2.a.b 1
1862.2.a.c 1
1862.2.a.d 1
1862.2.a.e 1
1862.2.a.f 1
1862.2.a.g 2
1862.2.a.h 2
1862.2.a.i 2
1862.2.a.j 2
1862.2.a.k 2
1862.2.a.l 2
1862.2.a.m 2
1862.2.a.n 3
1862.2.a.o 3
1862.2.a.p 3
1862.2.a.q 3
1862.2.a.r 3
1862.2.a.s 4
1862.2.a.t 4
1862.2.a.u 4
1862.2.a.v 4
1862.2.a.w 5
1862.2.a.x 5
1862.2.d $$\chi_{1862}(1861, \cdot)$$ 1862.2.d.a 24 1
1862.2.d.b 40
1862.2.e $$\chi_{1862}(1255, \cdot)$$ n/a 120 2
1862.2.f $$\chi_{1862}(197, \cdot)$$ n/a 134 2
1862.2.g $$\chi_{1862}(1341, \cdot)$$ n/a 136 2
1862.2.h $$\chi_{1862}(961, \cdot)$$ n/a 136 2
1862.2.k $$\chi_{1862}(411, \cdot)$$ n/a 136 2
1862.2.l $$\chi_{1862}(227, \cdot)$$ n/a 136 2
1862.2.m $$\chi_{1862}(293, \cdot)$$ n/a 128 2
1862.2.t $$\chi_{1862}(31, \cdot)$$ n/a 136 2
1862.2.u $$\chi_{1862}(267, \cdot)$$ n/a 504 6
1862.2.v $$\chi_{1862}(99, \cdot)$$ n/a 414 6
1862.2.w $$\chi_{1862}(177, \cdot)$$ n/a 396 6
1862.2.x $$\chi_{1862}(557, \cdot)$$ n/a 396 6
1862.2.y $$\chi_{1862}(265, \cdot)$$ n/a 576 6
1862.2.bb $$\chi_{1862}(97, \cdot)$$ n/a 408 6
1862.2.bc $$\chi_{1862}(325, \cdot)$$ n/a 396 6
1862.2.bh $$\chi_{1862}(117, \cdot)$$ n/a 396 6
1862.2.bk $$\chi_{1862}(163, \cdot)$$ n/a 1104 12
1862.2.bl $$\chi_{1862}(11, \cdot)$$ n/a 1104 12
1862.2.bm $$\chi_{1862}(239, \cdot)$$ n/a 1152 12
1862.2.bn $$\chi_{1862}(39, \cdot)$$ n/a 1008 12
1862.2.bo $$\chi_{1862}(103, \cdot)$$ n/a 1104 12
1862.2.bv $$\chi_{1862}(27, \cdot)$$ n/a 1152 12
1862.2.bw $$\chi_{1862}(75, \cdot)$$ n/a 1104 12
1862.2.bx $$\chi_{1862}(145, \cdot)$$ n/a 1104 12
1862.2.ca $$\chi_{1862}(25, \cdot)$$ n/a 3384 36
1862.2.cb $$\chi_{1862}(43, \cdot)$$ n/a 3312 36
1862.2.cc $$\chi_{1862}(9, \cdot)$$ n/a 3384 36
1862.2.cf $$\chi_{1862}(33, \cdot)$$ n/a 3384 36
1862.2.ck $$\chi_{1862}(13, \cdot)$$ n/a 3312 36
1862.2.cl $$\chi_{1862}(3, \cdot)$$ n/a 3384 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1862))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1862)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$$$^{\oplus 2}$$