# Properties

 Label 1900.3 Level 1900 Weight 3 Dimension 114788 Nonzero newspaces 36 Sturm bound 648000 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$36$$ Sturm bound: $$648000$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1900))$$.

Total New Old
Modular forms 218520 116180 102340
Cusp forms 213480 114788 98692
Eisenstein series 5040 1392 3648

## Trace form

 $$114788q - 105q^{2} + 8q^{3} - 113q^{4} - 268q^{5} - 217q^{6} - 56q^{7} - 129q^{8} - 226q^{9} + O(q^{10})$$ $$114788q - 105q^{2} + 8q^{3} - 113q^{4} - 268q^{5} - 217q^{6} - 56q^{7} - 129q^{8} - 226q^{9} - 112q^{10} + 80q^{11} + 63q^{12} - 126q^{13} + 127q^{14} + 4q^{15} + 39q^{16} - 413q^{17} - 18q^{18} - 121q^{19} - 356q^{20} - 569q^{21} - 417q^{22} - 269q^{23} - 653q^{24} - 104q^{25} - 745q^{26} + 110q^{27} - 500q^{28} - 10q^{29} - 44q^{30} + 60q^{31} + 190q^{32} + 350q^{33} + 392q^{34} + 416q^{35} + 381q^{36} + 236q^{37} + 446q^{38} + 908q^{39} + 728q^{40} - 122q^{41} + 1273q^{42} + 615q^{43} + 598q^{44} - 48q^{45} + 68q^{46} + 271q^{47} + 856q^{48} - 463q^{49} - 132q^{50} + 127q^{51} - 413q^{52} - 1206q^{53} - 868q^{54} - 600q^{55} - 426q^{56} - 931q^{57} - 1618q^{58} - 1235q^{59} - 2244q^{60} - 1514q^{61} - 1132q^{62} - 2368q^{63} - 461q^{64} - 808q^{65} + 239q^{66} - 1135q^{67} - 200q^{68} - 221q^{69} - 284q^{70} + 67q^{71} - 160q^{72} + 961q^{73} - 857q^{74} + 36q^{75} - 559q^{76} - 367q^{77} - 831q^{78} - 1322q^{79} - 412q^{80} - 2704q^{81} - 1938q^{82} - 539q^{83} - 3341q^{84} + 832q^{85} - 1510q^{86} - 900q^{87} - 3033q^{88} + 1705q^{89} - 3052q^{90} - 60q^{91} - 2742q^{92} + 166q^{93} - 2734q^{94} + 332q^{95} - 3190q^{96} - 115q^{97} - 1374q^{98} + 1638q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1900))$$

We only show spaces with odd 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
1900.3.b $$\chi_{1900}(951, \cdot)$$ n/a 342 1
1900.3.e $$\chi_{1900}(1101, \cdot)$$ 1900.3.e.a 2 1
1900.3.e.b 2
1900.3.e.c 4
1900.3.e.d 4
1900.3.e.e 12
1900.3.e.f 12
1900.3.e.g 14
1900.3.e.h 14
1900.3.g $$\chi_{1900}(949, \cdot)$$ 1900.3.g.a 4 1
1900.3.g.b 4
1900.3.g.c 24
1900.3.g.d 28
1900.3.h $$\chi_{1900}(799, \cdot)$$ n/a 324 1
1900.3.j $$\chi_{1900}(607, \cdot)$$ n/a 712 2
1900.3.m $$\chi_{1900}(457, \cdot)$$ n/a 108 2
1900.3.p $$\chi_{1900}(449, \cdot)$$ n/a 120 2
1900.3.q $$\chi_{1900}(999, \cdot)$$ n/a 712 2
1900.3.r $$\chi_{1900}(1151, \cdot)$$ n/a 748 2
1900.3.u $$\chi_{1900}(601, \cdot)$$ n/a 128 2
1900.3.w $$\chi_{1900}(189, \cdot)$$ n/a 400 4
1900.3.y $$\chi_{1900}(39, \cdot)$$ n/a 2160 4
1900.3.ba $$\chi_{1900}(191, \cdot)$$ n/a 2160 4
1900.3.bb $$\chi_{1900}(341, \cdot)$$ n/a 400 4
1900.3.be $$\chi_{1900}(107, \cdot)$$ n/a 1424 4
1900.3.bf $$\chi_{1900}(657, \cdot)$$ n/a 240 4
1900.3.bi $$\chi_{1900}(401, \cdot)$$ n/a 378 6
1900.3.bj $$\chi_{1900}(99, \cdot)$$ n/a 2136 6
1900.3.bl $$\chi_{1900}(249, \cdot)$$ n/a 360 6
1900.3.bo $$\chi_{1900}(251, \cdot)$$ n/a 2244 6
1900.3.bp $$\chi_{1900}(77, \cdot)$$ n/a 720 8
1900.3.bs $$\chi_{1900}(227, \cdot)$$ n/a 4768 8
1900.3.bu $$\chi_{1900}(11, \cdot)$$ n/a 4768 8
1900.3.bv $$\chi_{1900}(141, \cdot)$$ n/a 800 8
1900.3.bx $$\chi_{1900}(69, \cdot)$$ n/a 800 8
1900.3.bz $$\chi_{1900}(159, \cdot)$$ n/a 4768 8
1900.3.ca $$\chi_{1900}(93, \cdot)$$ n/a 720 12
1900.3.cc $$\chi_{1900}(143, \cdot)$$ n/a 4272 12
1900.3.cg $$\chi_{1900}(197, \cdot)$$ n/a 1600 16
1900.3.ch $$\chi_{1900}(27, \cdot)$$ n/a 9536 16
1900.3.ck $$\chi_{1900}(119, \cdot)$$ n/a 14304 24
1900.3.cl $$\chi_{1900}(21, \cdot)$$ n/a 2400 24
1900.3.cm $$\chi_{1900}(111, \cdot)$$ n/a 14304 24
1900.3.cp $$\chi_{1900}(29, \cdot)$$ n/a 2400 24
1900.3.cr $$\chi_{1900}(3, \cdot)$$ n/a 28608 48
1900.3.ct $$\chi_{1900}(17, \cdot)$$ n/a 4800 48

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1900))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1900)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 2}$$