# Properties

 Label 2070.4 Level 2070 Weight 4 Dimension 82450 Nonzero newspaces 24 Sturm bound 912384 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$912384$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2070))$$.

Total New Old
Modular forms 344960 82450 262510
Cusp forms 339328 82450 256878
Eisenstein series 5632 0 5632

## Trace form

 $$82450 q + 12 q^{2} + 12 q^{3} - 24 q^{4} + 34 q^{5} - 72 q^{6} - 8 q^{7} - 48 q^{8} - 164 q^{9} + O(q^{10})$$ $$82450 q + 12 q^{2} + 12 q^{3} - 24 q^{4} + 34 q^{5} - 72 q^{6} - 8 q^{7} - 48 q^{8} - 164 q^{9} + 68 q^{10} + 68 q^{11} - 32 q^{12} - 596 q^{13} - 400 q^{14} - 492 q^{15} - 224 q^{16} - 1060 q^{17} + 560 q^{18} + 1704 q^{19} + 840 q^{20} + 1440 q^{21} + 2096 q^{22} + 2284 q^{23} - 96 q^{24} + 262 q^{25} - 688 q^{26} - 1104 q^{27} - 960 q^{28} - 4636 q^{29} - 576 q^{30} - 4096 q^{31} + 192 q^{32} - 572 q^{33} + 1648 q^{34} - 1686 q^{35} + 1168 q^{36} + 2356 q^{37} + 1944 q^{38} + 1864 q^{39} - 240 q^{40} + 5356 q^{41} + 1600 q^{42} + 988 q^{43} - 1280 q^{44} + 5636 q^{45} - 1712 q^{46} + 8080 q^{47} + 448 q^{48} + 3750 q^{49} + 1468 q^{50} + 60 q^{51} + 880 q^{52} - 2392 q^{53} + 11896 q^{54} + 13564 q^{55} + 10528 q^{56} + 8396 q^{57} + 14424 q^{58} + 2992 q^{59} + 480 q^{60} + 4796 q^{61} - 10392 q^{62} - 21512 q^{63} + 1920 q^{64} - 23736 q^{65} - 20864 q^{66} - 7988 q^{67} - 18912 q^{68} - 29148 q^{69} - 24480 q^{70} - 56856 q^{71} - 9952 q^{72} - 15908 q^{73} - 24424 q^{74} - 17488 q^{75} - 8816 q^{76} - 15360 q^{77} + 1376 q^{78} + 3516 q^{79} + 3040 q^{80} + 29292 q^{81} + 17544 q^{82} + 61652 q^{83} + 18880 q^{84} + 25490 q^{85} + 46384 q^{86} + 16720 q^{87} + 4512 q^{88} + 36648 q^{89} + 13888 q^{90} + 43656 q^{91} + 1392 q^{92} + 11672 q^{93} + 6608 q^{94} + 20096 q^{95} + 1024 q^{96} + 21636 q^{97} + 13028 q^{98} - 5024 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2070))$$

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
2070.4.a $$\chi_{2070}(1, \cdot)$$ 2070.4.a.a 1 1
2070.4.a.b 1
2070.4.a.c 1
2070.4.a.d 1
2070.4.a.e 1
2070.4.a.f 1
2070.4.a.g 1
2070.4.a.h 1
2070.4.a.i 1
2070.4.a.j 1
2070.4.a.k 1
2070.4.a.l 1
2070.4.a.m 1
2070.4.a.n 1
2070.4.a.o 1
2070.4.a.p 2
2070.4.a.q 2
2070.4.a.r 2
2070.4.a.s 2
2070.4.a.t 2
2070.4.a.u 3
2070.4.a.v 3
2070.4.a.w 3
2070.4.a.x 3
2070.4.a.y 3
2070.4.a.z 3
2070.4.a.ba 3
2070.4.a.bb 3
2070.4.a.bc 3
2070.4.a.bd 3
2070.4.a.be 3
2070.4.a.bf 4
2070.4.a.bg 4
2070.4.a.bh 4
2070.4.a.bi 4
2070.4.a.bj 4
2070.4.a.bk 5
2070.4.a.bl 5
2070.4.a.bm 5
2070.4.a.bn 5
2070.4.a.bo 6
2070.4.a.bp 6
2070.4.d $$\chi_{2070}(829, \cdot)$$ n/a 164 1
2070.4.e $$\chi_{2070}(1241, \cdot)$$ 2070.4.e.a 48 1
2070.4.e.b 48
2070.4.h $$\chi_{2070}(2069, \cdot)$$ n/a 144 1
2070.4.i $$\chi_{2070}(691, \cdot)$$ n/a 528 2
2070.4.j $$\chi_{2070}(323, \cdot)$$ n/a 264 2
2070.4.k $$\chi_{2070}(1333, \cdot)$$ n/a 360 2
2070.4.n $$\chi_{2070}(689, \cdot)$$ n/a 864 2
2070.4.q $$\chi_{2070}(551, \cdot)$$ n/a 576 2
2070.4.r $$\chi_{2070}(139, \cdot)$$ n/a 792 2
2070.4.u $$\chi_{2070}(271, \cdot)$$ n/a 1200 10
2070.4.x $$\chi_{2070}(47, \cdot)$$ n/a 1584 4
2070.4.y $$\chi_{2070}(367, \cdot)$$ n/a 1728 4
2070.4.z $$\chi_{2070}(89, \cdot)$$ n/a 1440 10
2070.4.bc $$\chi_{2070}(251, \cdot)$$ n/a 960 10
2070.4.bd $$\chi_{2070}(289, \cdot)$$ n/a 1800 10
2070.4.bg $$\chi_{2070}(31, \cdot)$$ n/a 5760 20
2070.4.bj $$\chi_{2070}(37, \cdot)$$ n/a 3600 20
2070.4.bk $$\chi_{2070}(197, \cdot)$$ n/a 2880 20
2070.4.bn $$\chi_{2070}(49, \cdot)$$ n/a 8640 20
2070.4.bo $$\chi_{2070}(11, \cdot)$$ n/a 5760 20
2070.4.br $$\chi_{2070}(149, \cdot)$$ n/a 8640 20
2070.4.bs $$\chi_{2070}(7, \cdot)$$ n/a 17280 40
2070.4.bt $$\chi_{2070}(77, \cdot)$$ n/a 17280 40

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2070))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2070)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1035))$$$$^{\oplus 2}$$