## Defining parameters

 Level: $$N$$ = $$2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$456192$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2070))$$.

Total New Old
Modular forms 116864 27482 89382
Cusp forms 111233 27482 83751
Eisenstein series 5631 0 5631

## Trace form

 $$27482q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + O(q^{10})$$ $$27482q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + 22q^{10} + 52q^{11} + 16q^{12} + 28q^{13} + 40q^{14} + 48q^{15} - 6q^{16} - 8q^{17} + 8q^{18} - 28q^{19} + 72q^{21} - 24q^{22} - 52q^{23} - 12q^{24} - 10q^{25} - 56q^{26} + 48q^{27} - 44q^{28} - 32q^{29} - 28q^{31} - 6q^{32} - 20q^{33} - 8q^{34} - 54q^{35} - 20q^{36} - 36q^{37} - 84q^{38} - 128q^{39} + 6q^{40} - 196q^{41} - 128q^{42} - 108q^{43} - 64q^{44} - 160q^{45} - 208q^{47} - 20q^{48} - 138q^{49} - 94q^{50} - 60q^{51} - 20q^{52} - 104q^{53} + 28q^{54} + 128q^{55} + 92q^{56} + 212q^{57} + 196q^{58} + 464q^{59} + 60q^{60} + 500q^{61} + 396q^{62} + 520q^{63} + 6q^{64} + 546q^{65} + 448q^{66} + 300q^{67} + 336q^{68} + 504q^{69} + 312q^{70} + 804q^{71} + 188q^{72} + 380q^{73} + 628q^{74} + 296q^{75} + 92q^{76} + 684q^{77} + 320q^{78} + 548q^{79} + 56q^{80} + 348q^{81} + 380q^{82} + 280q^{83} + 112q^{84} + 170q^{85} + 272q^{86} + 40q^{87} + 20q^{88} + 48q^{89} + 112q^{90} + 40q^{91} + 36q^{92} - 64q^{93} + 56q^{94} - 2q^{95} + 16q^{96} + 176q^{97} + 142q^{98} + 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2070))$$

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
2070.2.a $$\chi_{2070}(1, \cdot)$$ 2070.2.a.a 1 1
2070.2.a.b 1
2070.2.a.c 1
2070.2.a.d 1
2070.2.a.e 1
2070.2.a.f 1
2070.2.a.g 1
2070.2.a.h 1
2070.2.a.i 1
2070.2.a.j 1
2070.2.a.k 1
2070.2.a.l 1
2070.2.a.m 1
2070.2.a.n 1
2070.2.a.o 1
2070.2.a.p 1
2070.2.a.q 1
2070.2.a.r 1
2070.2.a.s 1
2070.2.a.t 2
2070.2.a.u 2
2070.2.a.v 2
2070.2.a.w 2
2070.2.a.x 2
2070.2.a.y 2
2070.2.a.z 3
2070.2.d $$\chi_{2070}(829, \cdot)$$ 2070.2.d.a 4 1
2070.2.d.b 4
2070.2.d.c 4
2070.2.d.d 6
2070.2.d.e 6
2070.2.d.f 8
2070.2.d.g 8
2070.2.d.h 16
2070.2.e $$\chi_{2070}(1241, \cdot)$$ 2070.2.e.a 16 1
2070.2.e.b 16
2070.2.h $$\chi_{2070}(2069, \cdot)$$ 2070.2.h.a 24 1
2070.2.h.b 24
2070.2.i $$\chi_{2070}(691, \cdot)$$ n/a 176 2
2070.2.j $$\chi_{2070}(323, \cdot)$$ 2070.2.j.a 4 2
2070.2.j.b 4
2070.2.j.c 4
2070.2.j.d 4
2070.2.j.e 4
2070.2.j.f 4
2070.2.j.g 12
2070.2.j.h 16
2070.2.j.i 16
2070.2.j.j 20
2070.2.k $$\chi_{2070}(1333, \cdot)$$ n/a 120 2
2070.2.n $$\chi_{2070}(689, \cdot)$$ n/a 288 2
2070.2.q $$\chi_{2070}(551, \cdot)$$ n/a 192 2
2070.2.r $$\chi_{2070}(139, \cdot)$$ n/a 264 2
2070.2.u $$\chi_{2070}(271, \cdot)$$ n/a 400 10
2070.2.x $$\chi_{2070}(47, \cdot)$$ n/a 528 4
2070.2.y $$\chi_{2070}(367, \cdot)$$ n/a 576 4
2070.2.z $$\chi_{2070}(89, \cdot)$$ n/a 480 10
2070.2.bc $$\chi_{2070}(251, \cdot)$$ n/a 320 10
2070.2.bd $$\chi_{2070}(289, \cdot)$$ n/a 600 10
2070.2.bg $$\chi_{2070}(31, \cdot)$$ n/a 1920 20
2070.2.bj $$\chi_{2070}(37, \cdot)$$ n/a 1200 20
2070.2.bk $$\chi_{2070}(197, \cdot)$$ n/a 960 20
2070.2.bn $$\chi_{2070}(49, \cdot)$$ n/a 2880 20
2070.2.bo $$\chi_{2070}(11, \cdot)$$ n/a 1920 20
2070.2.br $$\chi_{2070}(149, \cdot)$$ n/a 2880 20
2070.2.bs $$\chi_{2070}(7, \cdot)$$ n/a 5760 40
2070.2.bt $$\chi_{2070}(77, \cdot)$$ n/a 5760 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2070))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2070)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1035))$$$$^{\oplus 2}$$