# Properties

 Label 2057.4 Level 2057 Weight 4 Dimension 508438 Nonzero newspaces 20 Sturm bound 1393920 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$2057 = 11^{2} \cdot 17$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$20$$ Sturm bound: $$1393920$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2057))$$.

Total New Old
Modular forms 525280 512652 12628
Cusp forms 520160 508438 11722
Eisenstein series 5120 4214 906

## Trace form

 $$508438 q - 638 q^{2} - 638 q^{3} - 638 q^{4} - 638 q^{5} - 838 q^{6} - 678 q^{7} - 478 q^{8} - 318 q^{9} + O(q^{10})$$ $$508438 q - 638 q^{2} - 638 q^{3} - 638 q^{4} - 638 q^{5} - 838 q^{6} - 678 q^{7} - 478 q^{8} - 318 q^{9} - 362 q^{10} - 600 q^{11} - 654 q^{12} - 526 q^{13} - 1258 q^{14} - 1542 q^{15} - 1718 q^{16} - 855 q^{17} - 938 q^{18} + 342 q^{19} + 1214 q^{20} + 926 q^{21} + 560 q^{22} - 1806 q^{23} - 3270 q^{24} - 2106 q^{25} - 2370 q^{26} - 1274 q^{27} - 1154 q^{28} - 578 q^{29} - 794 q^{30} - 1334 q^{31} + 1438 q^{32} - 1110 q^{33} + 149 q^{34} - 94 q^{35} + 1206 q^{36} + 594 q^{37} + 574 q^{38} + 1226 q^{39} - 2954 q^{40} - 18 q^{41} - 3426 q^{42} - 4922 q^{43} - 2930 q^{44} + 1022 q^{45} + 1934 q^{46} + 3242 q^{47} + 8366 q^{48} + 4858 q^{49} + 2514 q^{50} + 107 q^{51} - 2874 q^{52} - 8866 q^{53} - 16146 q^{54} - 3900 q^{55} - 7918 q^{56} - 8346 q^{57} + 2702 q^{58} + 3758 q^{59} + 4766 q^{60} + 882 q^{61} + 7878 q^{62} + 2070 q^{63} + 66 q^{64} + 4122 q^{65} + 1910 q^{66} + 4338 q^{67} + 5667 q^{68} + 6078 q^{69} + 1214 q^{70} + 1434 q^{71} + 138 q^{72} - 10538 q^{73} - 6234 q^{74} - 2474 q^{75} + 630 q^{76} - 5160 q^{77} - 10062 q^{78} - 3150 q^{79} - 15322 q^{80} - 8882 q^{81} - 12974 q^{82} - 4034 q^{83} - 12242 q^{84} + 689 q^{85} - 6222 q^{86} + 11934 q^{87} + 8660 q^{88} + 5498 q^{89} - 2266 q^{90} + 6482 q^{91} - 7106 q^{92} - 9238 q^{93} + 2158 q^{94} + 9810 q^{95} + 6574 q^{96} + 3070 q^{97} + 15438 q^{98} + 2540 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2057))$$

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
2057.4.a $$\chi_{2057}(1, \cdot)$$ 2057.4.a.a 1 1
2057.4.a.b 1
2057.4.a.c 1
2057.4.a.d 1
2057.4.a.e 3
2057.4.a.f 3
2057.4.a.g 4
2057.4.a.h 10
2057.4.a.i 10
2057.4.a.j 12
2057.4.a.k 19
2057.4.a.l 19
2057.4.a.m 20
2057.4.a.n 20
2057.4.a.o 20
2057.4.a.p 20
2057.4.a.q 40
2057.4.a.r 40
2057.4.a.s 44
2057.4.a.t 44
2057.4.a.u 52
2057.4.a.v 52
2057.4.d $$\chi_{2057}(1937, \cdot)$$ n/a 482 1
2057.4.e $$\chi_{2057}(727, \cdot)$$ n/a 964 2
2057.4.g $$\chi_{2057}(511, \cdot)$$ n/a 1728 4
2057.4.h $$\chi_{2057}(485, \cdot)$$ n/a 1924 4
2057.4.j $$\chi_{2057}(390, \cdot)$$ n/a 1912 4
2057.4.m $$\chi_{2057}(188, \cdot)$$ n/a 5280 10
2057.4.n $$\chi_{2057}(241, \cdot)$$ n/a 3824 8
2057.4.q $$\chi_{2057}(81, \cdot)$$ n/a 3824 8
2057.4.r $$\chi_{2057}(67, \cdot)$$ n/a 5920 10
2057.4.v $$\chi_{2057}(9, \cdot)$$ n/a 7648 16
2057.4.x $$\chi_{2057}(89, \cdot)$$ n/a 11840 20
2057.4.y $$\chi_{2057}(69, \cdot)$$ n/a 21120 40
2057.4.ba $$\chi_{2057}(40, \cdot)$$ n/a 15296 32
2057.4.bc $$\chi_{2057}(100, \cdot)$$ n/a 23680 40
2057.4.bf $$\chi_{2057}(16, \cdot)$$ n/a 23680 40
2057.4.bh $$\chi_{2057}(10, \cdot)$$ n/a 47360 80
2057.4.bi $$\chi_{2057}(4, \cdot)$$ n/a 47360 80
2057.4.bk $$\chi_{2057}(15, \cdot)$$ n/a 94720 160
2057.4.bm $$\chi_{2057}(6, \cdot)$$ n/a 189440 320

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2057))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2057)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 2}$$