## Defining parameters

 Level: $$N$$ = $$1849 = 43^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Sturm bound: $$1138984$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1849))$$.

Total New Old
Modular forms 428463 427960 503
Cusp forms 425775 425355 420
Eisenstein series 2688 2605 83

## Trace form

 $$425355q - 861q^{2} - 861q^{3} - 861q^{4} - 861q^{5} - 861q^{6} - 861q^{7} - 861q^{8} - 861q^{9} + O(q^{10})$$ $$425355q - 861q^{2} - 861q^{3} - 861q^{4} - 861q^{5} - 861q^{6} - 861q^{7} - 861q^{8} - 861q^{9} - 861q^{10} - 861q^{11} - 861q^{12} - 861q^{13} - 861q^{14} - 861q^{15} - 861q^{16} - 861q^{17} - 861q^{18} - 861q^{19} - 861q^{20} - 861q^{21} - 861q^{22} - 861q^{23} - 861q^{24} - 861q^{25} - 861q^{26} - 861q^{27} - 861q^{28} - 861q^{29} - 861q^{30} + 399q^{31} + 4851q^{32} + 3171q^{33} + 2919q^{34} + 315q^{35} - 861q^{36} - 1869q^{37} - 4557q^{38} - 3801q^{39} - 12957q^{40} - 2541q^{41} - 7875q^{42} - 5292q^{43} - 8421q^{44} - 8421q^{45} - 5901q^{46} - 1785q^{47} - 4893q^{48} - 861q^{49} + 1491q^{50} + 1659q^{51} + 9891q^{52} + 4851q^{53} + 10479q^{54} + 8715q^{55} + 10899q^{56} + 1491q^{57} - 861q^{58} - 861q^{59} - 861q^{60} - 861q^{61} - 861q^{62} - 861q^{63} - 861q^{64} - 861q^{65} - 861q^{66} - 861q^{67} - 861q^{68} + 14847q^{69} + 25179q^{70} + 9639q^{71} + 39879q^{72} + 5103q^{73} + 12957q^{74} + 6489q^{75} + 609q^{76} - 4137q^{77} - 16695q^{78} - 8085q^{79} - 19341q^{80} - 22701q^{81} - 31521q^{82} - 14133q^{83} - 63273q^{84} - 15099q^{85} - 15162q^{86} - 36561q^{87} - 27069q^{88} - 13125q^{89} - 50001q^{90} - 10101q^{91} - 18921q^{92} - 10605q^{93} - 5229q^{94} - 21q^{95} + 12789q^{96} + 10983q^{97} + 20013q^{98} + 27657q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1849))$$

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
1849.4.a $$\chi_{1849}(1, \cdot)$$ 1849.4.a.a 1 1
1849.4.a.b 4
1849.4.a.c 6
1849.4.a.d 10
1849.4.a.e 10
1849.4.a.f 10
1849.4.a.g 30
1849.4.a.h 30
1849.4.a.i 50
1849.4.a.j 50
1849.4.a.k 60
1849.4.a.l 60
1849.4.a.m 110
1849.4.c $$\chi_{1849}(423, \cdot)$$ n/a 862 2
1849.4.e $$\chi_{1849}(78, \cdot)$$ n/a 2586 6
1849.4.g $$\chi_{1849}(210, \cdot)$$ n/a 5172 12
1849.4.i $$\chi_{1849}(44, \cdot)$$ n/a 19824 42
1849.4.k $$\chi_{1849}(6, \cdot)$$ n/a 39648 84
1849.4.m $$\chi_{1849}(4, \cdot)$$ n/a 118944 252
1849.4.o $$\chi_{1849}(9, \cdot)$$ n/a 237888 504

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1849))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1849)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 2}$$