# Properties

 Label 1850.2 Level 1850 Weight 2 Dimension 31473 Nonzero newspaces 36 Sturm bound 410400 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1850 = 2 \cdot 5^{2} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$410400$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1850))$$.

Total New Old
Modular forms 104616 31473 73143
Cusp forms 100585 31473 69112
Eisenstein series 4031 0 4031

## Trace form

 $$31473 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10})$$ $$31473 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} - 16 q^{21} - 56 q^{22} - 32 q^{23} - 32 q^{24} - 70 q^{25} - 3 q^{26} + 8 q^{27} - 12 q^{28} + 16 q^{29} - 40 q^{30} + 92 q^{31} - 8 q^{32} + 88 q^{33} + 58 q^{34} + 40 q^{35} + 71 q^{36} + 117 q^{37} + 76 q^{38} + 116 q^{39} + 10 q^{40} + 152 q^{41} + 136 q^{42} + 80 q^{43} + 24 q^{44} - 30 q^{45} + 120 q^{46} + 52 q^{47} + 20 q^{48} + 72 q^{49} + 50 q^{50} + 24 q^{51} + 28 q^{52} + 18 q^{53} + 80 q^{54} + 40 q^{55} + 16 q^{56} + 60 q^{58} + 36 q^{59} + 49 q^{61} - 56 q^{62} + 36 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} + 12 q^{67} - 84 q^{68} + 56 q^{69} - 80 q^{70} + 56 q^{71} + 26 q^{72} + 60 q^{73} - 62 q^{74} - 120 q^{75} - 40 q^{76} - 56 q^{77} - 88 q^{78} + 72 q^{79} + 10 q^{80} + 226 q^{81} - 76 q^{82} - 116 q^{83} - 56 q^{84} - 30 q^{85} - 32 q^{86} + 68 q^{87} + 24 q^{88} + 15 q^{89} + 10 q^{90} + 112 q^{91} + 44 q^{92} + 244 q^{93} + 168 q^{94} + 120 q^{95} + 8 q^{96} + 300 q^{97} + 258 q^{98} + 372 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1850))$$

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
1850.2.a $$\chi_{1850}(1, \cdot)$$ 1850.2.a.a 1 1
1850.2.a.b 1
1850.2.a.c 1
1850.2.a.d 1
1850.2.a.e 1
1850.2.a.f 1
1850.2.a.g 1
1850.2.a.h 1
1850.2.a.i 1
1850.2.a.j 1
1850.2.a.k 1
1850.2.a.l 1
1850.2.a.m 1
1850.2.a.n 1
1850.2.a.o 1
1850.2.a.p 1
1850.2.a.q 2
1850.2.a.r 2
1850.2.a.s 2
1850.2.a.t 2
1850.2.a.u 2
1850.2.a.v 2
1850.2.a.w 2
1850.2.a.x 2
1850.2.a.y 3
1850.2.a.z 3
1850.2.a.ba 3
1850.2.a.bb 3
1850.2.a.bc 3
1850.2.a.bd 5
1850.2.a.be 5
1850.2.b $$\chi_{1850}(149, \cdot)$$ 1850.2.b.a 2 1
1850.2.b.b 2
1850.2.b.c 2
1850.2.b.d 2
1850.2.b.e 2
1850.2.b.f 2
1850.2.b.g 2
1850.2.b.h 2
1850.2.b.i 4
1850.2.b.j 4
1850.2.b.k 4
1850.2.b.l 4
1850.2.b.m 4
1850.2.b.n 6
1850.2.b.o 6
1850.2.b.p 6
1850.2.c $$\chi_{1850}(1849, \cdot)$$ 1850.2.c.a 2 1
1850.2.c.b 2
1850.2.c.c 2
1850.2.c.d 2
1850.2.c.e 2
1850.2.c.f 2
1850.2.c.g 4
1850.2.c.h 4
1850.2.c.i 6
1850.2.c.j 6
1850.2.c.k 12
1850.2.c.l 12
1850.2.d $$\chi_{1850}(1701, \cdot)$$ 1850.2.d.a 2 1
1850.2.d.b 2
1850.2.d.c 2
1850.2.d.d 2
1850.2.d.e 4
1850.2.d.f 6
1850.2.d.g 12
1850.2.d.h 12
1850.2.d.i 20
1850.2.e $$\chi_{1850}(951, \cdot)$$ n/a 122 2
1850.2.g $$\chi_{1850}(43, \cdot)$$ n/a 114 2
1850.2.h $$\chi_{1850}(857, \cdot)$$ n/a 114 2
1850.2.l $$\chi_{1850}(371, \cdot)$$ n/a 360 4
1850.2.m $$\chi_{1850}(101, \cdot)$$ n/a 124 2
1850.2.n $$\chi_{1850}(249, \cdot)$$ n/a 112 2
1850.2.o $$\chi_{1850}(1099, \cdot)$$ n/a 116 2
1850.2.p $$\chi_{1850}(201, \cdot)$$ n/a 354 6
1850.2.q $$\chi_{1850}(221, \cdot)$$ n/a 376 4
1850.2.r $$\chi_{1850}(369, \cdot)$$ n/a 384 4
1850.2.s $$\chi_{1850}(519, \cdot)$$ n/a 360 4
1850.2.u $$\chi_{1850}(643, \cdot)$$ n/a 228 4
1850.2.v $$\chi_{1850}(193, \cdot)$$ n/a 228 4
1850.2.z $$\chi_{1850}(121, \cdot)$$ n/a 768 8
1850.2.ba $$\chi_{1850}(99, \cdot)$$ n/a 336 6
1850.2.bb $$\chi_{1850}(151, \cdot)$$ n/a 360 6
1850.2.bc $$\chi_{1850}(49, \cdot)$$ n/a 348 6
1850.2.bg $$\chi_{1850}(117, \cdot)$$ n/a 760 8
1850.2.bh $$\chi_{1850}(327, \cdot)$$ n/a 760 8
1850.2.bj $$\chi_{1850}(269, \cdot)$$ n/a 752 8
1850.2.bk $$\chi_{1850}(159, \cdot)$$ n/a 768 8
1850.2.bl $$\chi_{1850}(11, \cdot)$$ n/a 752 8
1850.2.bo $$\chi_{1850}(143, \cdot)$$ n/a 684 12
1850.2.br $$\chi_{1850}(57, \cdot)$$ n/a 684 12
1850.2.bs $$\chi_{1850}(71, \cdot)$$ n/a 2304 24
1850.2.bw $$\chi_{1850}(23, \cdot)$$ n/a 1520 16
1850.2.bx $$\chi_{1850}(97, \cdot)$$ n/a 1520 16
1850.2.bz $$\chi_{1850}(9, \cdot)$$ n/a 2256 24
1850.2.ca $$\chi_{1850}(21, \cdot)$$ n/a 2256 24
1850.2.cb $$\chi_{1850}(139, \cdot)$$ n/a 2304 24
1850.2.cc $$\chi_{1850}(13, \cdot)$$ n/a 4560 48
1850.2.cf $$\chi_{1850}(17, \cdot)$$ n/a 4560 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1850))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1850)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(925))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1850))$$$$^{\oplus 1}$$