# Properties

 Label 2028.4 Level 2028 Weight 4 Dimension 146891 Nonzero newspaces 24 Sturm bound 908544 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$2028 = 2^{2} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$908544$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2028))$$.

Total New Old
Modular forms 342984 147711 195273
Cusp forms 338424 146891 191533
Eisenstein series 4560 820 3740

## Trace form

 $$146891 q + 3 q^{3} - 140 q^{4} - 18 q^{5} - 90 q^{6} - 136 q^{7} - 135 q^{9} + O(q^{10})$$ $$146891 q + 3 q^{3} - 140 q^{4} - 18 q^{5} - 90 q^{6} - 136 q^{7} - 135 q^{9} - 52 q^{10} + 276 q^{11} + 66 q^{12} + 90 q^{15} - 356 q^{16} + 390 q^{17} + 810 q^{18} - 244 q^{19} + 480 q^{20} - 468 q^{21} - 1452 q^{22} - 840 q^{23} - 1986 q^{24} - 1337 q^{25} - 1500 q^{26} - 1629 q^{27} - 2652 q^{28} - 1014 q^{29} - 786 q^{30} + 224 q^{31} + 2040 q^{32} + 696 q^{33} + 4700 q^{34} + 2976 q^{35} + 3018 q^{36} + 274 q^{37} - 492 q^{39} - 7708 q^{40} + 7878 q^{41} - 2310 q^{42} + 1796 q^{43} - 600 q^{44} + 582 q^{45} + 4236 q^{46} - 1056 q^{47} + 3198 q^{48} - 13091 q^{49} + 10584 q^{50} - 2394 q^{51} + 5364 q^{52} - 9906 q^{53} + 822 q^{54} - 6264 q^{55} + 6696 q^{56} - 4224 q^{57} + 236 q^{58} + 2004 q^{59} - 5046 q^{60} + 7906 q^{61} - 7080 q^{62} - 456 q^{63} - 13820 q^{64} + 11718 q^{65} - 13158 q^{66} + 8924 q^{67} + 5484 q^{69} - 2652 q^{70} + 696 q^{71} + 6306 q^{72} - 902 q^{73} + 2157 q^{75} + 2028 q^{76} - 12960 q^{77} + 8706 q^{78} - 10528 q^{79} - 1647 q^{81} - 1252 q^{82} + 1260 q^{83} + 1458 q^{84} + 3904 q^{85} - 19488 q^{86} + 3666 q^{87} - 19452 q^{88} + 2682 q^{89} - 24942 q^{90} + 4680 q^{91} - 4176 q^{92} - 4404 q^{93} + 1020 q^{94} + 8520 q^{95} + 930 q^{96} + 17938 q^{97} + 15768 q^{98} + 7164 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2028))$$

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
2028.4.a $$\chi_{2028}(1, \cdot)$$ 2028.4.a.a 1 1
2028.4.a.b 1
2028.4.a.c 1
2028.4.a.d 2
2028.4.a.e 2
2028.4.a.f 2
2028.4.a.g 2
2028.4.a.h 2
2028.4.a.i 2
2028.4.a.j 4
2028.4.a.k 4
2028.4.a.l 4
2028.4.a.m 4
2028.4.a.n 4
2028.4.a.o 6
2028.4.a.p 9
2028.4.a.q 9
2028.4.a.r 9
2028.4.a.s 9
2028.4.b $$\chi_{2028}(337, \cdot)$$ 2028.4.b.a 2 1
2028.4.b.b 2
2028.4.b.c 2
2028.4.b.d 2
2028.4.b.e 4
2028.4.b.f 4
2028.4.b.g 4
2028.4.b.h 6
2028.4.b.i 8
2028.4.b.j 8
2028.4.b.k 18
2028.4.b.l 18
2028.4.c $$\chi_{2028}(1691, \cdot)$$ n/a 908 1
2028.4.h $$\chi_{2028}(2027, \cdot)$$ n/a 904 1
2028.4.i $$\chi_{2028}(529, \cdot)$$ n/a 152 2
2028.4.k $$\chi_{2028}(775, \cdot)$$ n/a 924 2
2028.4.m $$\chi_{2028}(437, \cdot)$$ n/a 308 2
2028.4.p $$\chi_{2028}(191, \cdot)$$ n/a 1808 2
2028.4.q $$\chi_{2028}(361, \cdot)$$ n/a 156 2
2028.4.r $$\chi_{2028}(23, \cdot)$$ n/a 1808 2
2028.4.u $$\chi_{2028}(89, \cdot)$$ n/a 616 4
2028.4.w $$\chi_{2028}(19, \cdot)$$ n/a 1848 4
2028.4.y $$\chi_{2028}(157, \cdot)$$ n/a 1104 12
2028.4.z $$\chi_{2028}(155, \cdot)$$ n/a 13056 12
2028.4.be $$\chi_{2028}(131, \cdot)$$ n/a 13056 12
2028.4.bf $$\chi_{2028}(25, \cdot)$$ n/a 1080 12
2028.4.bg $$\chi_{2028}(61, \cdot)$$ n/a 2208 24
2028.4.bi $$\chi_{2028}(5, \cdot)$$ n/a 4368 24
2028.4.bk $$\chi_{2028}(31, \cdot)$$ n/a 13104 24
2028.4.bn $$\chi_{2028}(95, \cdot)$$ n/a 26112 24
2028.4.bo $$\chi_{2028}(49, \cdot)$$ n/a 2160 24
2028.4.bp $$\chi_{2028}(35, \cdot)$$ n/a 26112 24
2028.4.bs $$\chi_{2028}(7, \cdot)$$ n/a 26208 48
2028.4.bu $$\chi_{2028}(41, \cdot)$$ n/a 8736 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2028))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2028)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(676))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1014))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2028))$$$$^{\oplus 1}$$