# Properties

 Label 1550.2 Level 1550 Weight 2 Dimension 22072 Nonzero newspaces 42 Sturm bound 288000 Trace bound 12

## Defining parameters

 Level: $$N$$ = $$1550 = 2 \cdot 5^{2} \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$288000$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1550))$$.

Total New Old
Modular forms 73680 22072 51608
Cusp forms 70321 22072 48249
Eisenstein series 3359 0 3359

## Trace form

 $$22072 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10})$$ $$22072 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} - 6 q^{21} - 26 q^{22} - 2 q^{23} - 32 q^{24} - 70 q^{25} + 18 q^{26} + 50 q^{27} + 16 q^{28} + 40 q^{29} - 40 q^{30} + 52 q^{31} - 8 q^{32} + 76 q^{33} + 46 q^{34} + 40 q^{35} + 66 q^{36} + 156 q^{37} + 70 q^{38} + 102 q^{39} + 10 q^{40} + 74 q^{41} + 94 q^{42} + 18 q^{43} + 24 q^{44} - 30 q^{45} + 48 q^{46} + 16 q^{47} + 8 q^{48} + 54 q^{49} + 50 q^{50} + 114 q^{51} + 28 q^{52} + 48 q^{53} + 80 q^{54} + 40 q^{55} + 16 q^{56} + 90 q^{57} + 60 q^{58} + 30 q^{59} + 94 q^{61} - 28 q^{62} + 48 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} + 6 q^{67} - 84 q^{68} + 2 q^{69} - 80 q^{70} + 44 q^{71} + 26 q^{72} + 18 q^{73} - 124 q^{74} - 120 q^{75} - 30 q^{76} - 8 q^{77} + 2 q^{78} + 70 q^{79} + 10 q^{80} + 202 q^{81} - 16 q^{82} + 58 q^{83} + 4 q^{84} - 30 q^{85} + 88 q^{86} + 80 q^{87} + 84 q^{88} + 120 q^{89} + 10 q^{90} + 194 q^{91} + 8 q^{92} + 308 q^{93} + 156 q^{94} + 120 q^{95} + 8 q^{96} + 286 q^{97} + 294 q^{98} + 342 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1550))$$

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
1550.2.a $$\chi_{1550}(1, \cdot)$$ 1550.2.a.a 1 1
1550.2.a.b 1
1550.2.a.c 1
1550.2.a.d 1
1550.2.a.e 1
1550.2.a.f 1
1550.2.a.g 1
1550.2.a.h 2
1550.2.a.i 2
1550.2.a.j 2
1550.2.a.k 3
1550.2.a.l 3
1550.2.a.m 3
1550.2.a.n 4
1550.2.a.o 4
1550.2.a.p 4
1550.2.a.q 4
1550.2.a.r 5
1550.2.a.s 5
1550.2.b $$\chi_{1550}(249, \cdot)$$ 1550.2.b.a 2 1
1550.2.b.b 2
1550.2.b.c 2
1550.2.b.d 2
1550.2.b.e 2
1550.2.b.f 4
1550.2.b.g 4
1550.2.b.h 4
1550.2.b.i 6
1550.2.b.j 6
1550.2.b.k 10
1550.2.e $$\chi_{1550}(501, \cdot)$$ 1550.2.e.a 2 2
1550.2.e.b 2
1550.2.e.c 2
1550.2.e.d 2
1550.2.e.e 2
1550.2.e.f 2
1550.2.e.g 2
1550.2.e.h 2
1550.2.e.i 4
1550.2.e.j 4
1550.2.e.k 6
1550.2.e.l 6
1550.2.e.m 6
1550.2.e.n 6
1550.2.e.o 10
1550.2.e.p 10
1550.2.e.q 16
1550.2.e.r 16
1550.2.f $$\chi_{1550}(557, \cdot)$$ 1550.2.f.a 16 2
1550.2.f.b 32
1550.2.f.c 48
1550.2.h $$\chi_{1550}(531, \cdot)$$ n/a 320 4
1550.2.i $$\chi_{1550}(101, \cdot)$$ n/a 208 4
1550.2.j $$\chi_{1550}(171, \cdot)$$ n/a 320 4
1550.2.k $$\chi_{1550}(221, \cdot)$$ n/a 320 4
1550.2.l $$\chi_{1550}(311, \cdot)$$ n/a 296 4
1550.2.m $$\chi_{1550}(411, \cdot)$$ n/a 320 4
1550.2.p $$\chi_{1550}(149, \cdot)$$ 1550.2.p.a 4 2
1550.2.p.b 4
1550.2.p.c 4
1550.2.p.d 4
1550.2.p.e 4
1550.2.p.f 8
1550.2.p.g 12
1550.2.p.h 12
1550.2.p.i 12
1550.2.p.j 12
1550.2.p.k 20
1550.2.r $$\chi_{1550}(39, \cdot)$$ n/a 320 4
1550.2.x $$\chi_{1550}(559, \cdot)$$ n/a 304 4
1550.2.bc $$\chi_{1550}(109, \cdot)$$ n/a 320 4
1550.2.bd $$\chi_{1550}(349, \cdot)$$ n/a 192 4
1550.2.be $$\chi_{1550}(469, \cdot)$$ n/a 320 4
1550.2.bf $$\chi_{1550}(219, \cdot)$$ n/a 320 4
1550.2.bj $$\chi_{1550}(57, \cdot)$$ n/a 192 4
1550.2.bk $$\chi_{1550}(431, \cdot)$$ n/a 640 8
1550.2.bl $$\chi_{1550}(191, \cdot)$$ n/a 640 8
1550.2.bm $$\chi_{1550}(231, \cdot)$$ n/a 640 8
1550.2.bn $$\chi_{1550}(81, \cdot)$$ n/a 640 8
1550.2.bo $$\chi_{1550}(51, \cdot)$$ n/a 400 8
1550.2.bp $$\chi_{1550}(41, \cdot)$$ n/a 640 8
1550.2.bq $$\chi_{1550}(23, \cdot)$$ n/a 640 8
1550.2.bx $$\chi_{1550}(27, \cdot)$$ n/a 640 8
1550.2.by $$\chi_{1550}(123, \cdot)$$ n/a 640 8
1550.2.bz $$\chi_{1550}(263, \cdot)$$ n/a 640 8
1550.2.ca $$\chi_{1550}(457, \cdot)$$ n/a 384 8
1550.2.cb $$\chi_{1550}(77, \cdot)$$ n/a 640 8
1550.2.ce $$\chi_{1550}(9, \cdot)$$ n/a 640 8
1550.2.cf $$\chi_{1550}(69, \cdot)$$ n/a 640 8
1550.2.cg $$\chi_{1550}(49, \cdot)$$ n/a 384 8
1550.2.ch $$\chi_{1550}(59, \cdot)$$ n/a 640 8
1550.2.cm $$\chi_{1550}(129, \cdot)$$ n/a 640 8
1550.2.cs $$\chi_{1550}(329, \cdot)$$ n/a 640 8
1550.2.cu $$\chi_{1550}(53, \cdot)$$ n/a 1280 16
1550.2.cv $$\chi_{1550}(43, \cdot)$$ n/a 768 16
1550.2.cw $$\chi_{1550}(13, \cdot)$$ n/a 1280 16
1550.2.cx $$\chi_{1550}(37, \cdot)$$ n/a 1280 16
1550.2.cy $$\chi_{1550}(3, \cdot)$$ n/a 1280 16
1550.2.df $$\chi_{1550}(177, \cdot)$$ n/a 1280 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1550))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1550)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(775))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1550))$$$$^{\oplus 1}$$