## Defining parameters

 Level: $$N$$ = $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$432000$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1900))$$.

Total New Old
Modular forms 110520 58441 52079
Cusp forms 105481 57045 48436
Eisenstein series 5039 1396 3643

## Trace form

 $$57045q - 105q^{2} - 8q^{3} - 97q^{4} - 258q^{5} - 153q^{6} + 8q^{7} - 81q^{8} - 190q^{9} + O(q^{10})$$ $$57045q - 105q^{2} - 8q^{3} - 97q^{4} - 258q^{5} - 153q^{6} + 8q^{7} - 81q^{8} - 190q^{9} - 112q^{10} - 97q^{12} - 206q^{13} - 97q^{14} + 4q^{15} - 185q^{16} - 183q^{17} - 112q^{18} - 9q^{19} - 276q^{20} - 303q^{21} - 97q^{22} + 55q^{23} - 117q^{24} - 174q^{25} - 297q^{26} + 73q^{27} - 70q^{28} - 112q^{29} - 124q^{30} + 42q^{31} - 20q^{32} - 100q^{33} - 52q^{34} + 16q^{35} - 79q^{36} - 216q^{37} - 74q^{38} - 42q^{39} - 232q^{40} - 368q^{41} - 207q^{42} - 87q^{43} - 192q^{44} - 398q^{45} - 228q^{46} - 113q^{47} - 294q^{48} - 339q^{49} - 332q^{50} - 108q^{51} - 293q^{52} - 272q^{53} - 384q^{54} - 80q^{55} - 264q^{56} - 323q^{57} - 322q^{58} - 57q^{59} - 324q^{60} - 196q^{61} - 242q^{62} + 16q^{63} - 229q^{64} - 158q^{65} - 321q^{66} + 103q^{67} - 208q^{68} + 15q^{69} - 124q^{70} + 23q^{71} - 220q^{72} - 116q^{73} - 171q^{74} + 156q^{75} - 399q^{76} - 79q^{77} - 229q^{78} + 280q^{79} - 92q^{80} - 153q^{81} - 88q^{82} + 331q^{83} - 45q^{84} - 198q^{85} - 96q^{86} + 512q^{87} + 71q^{88} - 145q^{89} + 188q^{90} + 252q^{91} + 58q^{92} + 164q^{93} + 160q^{94} + 72q^{95} - 70q^{96} - 297q^{97} + 298q^{98} + 447q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1900))$$

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
1900.2.a $$\chi_{1900}(1, \cdot)$$ 1900.2.a.a 1 1
1900.2.a.b 1
1900.2.a.c 1
1900.2.a.d 2
1900.2.a.e 2
1900.2.a.f 3
1900.2.a.g 3
1900.2.a.h 3
1900.2.a.i 3
1900.2.a.j 4
1900.2.a.k 6
1900.2.c $$\chi_{1900}(1749, \cdot)$$ 1900.2.c.a 2 1
1900.2.c.b 2
1900.2.c.c 2
1900.2.c.d 4
1900.2.c.e 4
1900.2.c.f 6
1900.2.c.g 6
1900.2.d $$\chi_{1900}(1899, \cdot)$$ n/a 176 1
1900.2.f $$\chi_{1900}(151, \cdot)$$ n/a 184 1
1900.2.i $$\chi_{1900}(201, \cdot)$$ 1900.2.i.a 2 2
1900.2.i.b 2
1900.2.i.c 6
1900.2.i.d 8
1900.2.i.e 12
1900.2.i.f 12
1900.2.i.g 20
1900.2.k $$\chi_{1900}(343, \cdot)$$ n/a 324 2
1900.2.l $$\chi_{1900}(493, \cdot)$$ 1900.2.l.a 8 2
1900.2.l.b 12
1900.2.l.c 16
1900.2.l.d 24
1900.2.n $$\chi_{1900}(381, \cdot)$$ n/a 176 4
1900.2.o $$\chi_{1900}(1551, \cdot)$$ n/a 368 2
1900.2.s $$\chi_{1900}(49, \cdot)$$ 1900.2.s.a 4 2
1900.2.s.b 4
1900.2.s.c 12
1900.2.s.d 16
1900.2.s.e 24
1900.2.t $$\chi_{1900}(1399, \cdot)$$ n/a 352 2
1900.2.v $$\chi_{1900}(101, \cdot)$$ n/a 192 6
1900.2.x $$\chi_{1900}(531, \cdot)$$ n/a 1184 4
1900.2.z $$\chi_{1900}(229, \cdot)$$ n/a 184 4
1900.2.bc $$\chi_{1900}(379, \cdot)$$ n/a 1184 4
1900.2.bd $$\chi_{1900}(7, \cdot)$$ n/a 704 4
1900.2.bg $$\chi_{1900}(293, \cdot)$$ n/a 120 4
1900.2.bh $$\chi_{1900}(121, \cdot)$$ n/a 400 8
1900.2.bk $$\chi_{1900}(299, \cdot)$$ n/a 1056 6
1900.2.bm $$\chi_{1900}(149, \cdot)$$ n/a 180 6
1900.2.bn $$\chi_{1900}(51, \cdot)$$ n/a 1104 6
1900.2.bq $$\chi_{1900}(37, \cdot)$$ n/a 400 8
1900.2.br $$\chi_{1900}(267, \cdot)$$ n/a 2160 8
1900.2.bt $$\chi_{1900}(429, \cdot)$$ n/a 400 8
1900.2.bw $$\chi_{1900}(179, \cdot)$$ n/a 2368 8
1900.2.by $$\chi_{1900}(31, \cdot)$$ n/a 2368 8
1900.2.cb $$\chi_{1900}(193, \cdot)$$ n/a 360 12
1900.2.cd $$\chi_{1900}(43, \cdot)$$ n/a 2112 12
1900.2.ce $$\chi_{1900}(61, \cdot)$$ n/a 1200 24
1900.2.cf $$\chi_{1900}(217, \cdot)$$ n/a 800 16
1900.2.ci $$\chi_{1900}(83, \cdot)$$ n/a 4736 16
1900.2.cj $$\chi_{1900}(59, \cdot)$$ n/a 7104 24
1900.2.cn $$\chi_{1900}(71, \cdot)$$ n/a 7104 24
1900.2.co $$\chi_{1900}(9, \cdot)$$ n/a 1200 24
1900.2.cq $$\chi_{1900}(23, \cdot)$$ n/a 14208 48
1900.2.cs $$\chi_{1900}(13, \cdot)$$ n/a 2400 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1900))$$ into lower level spaces

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