# Properties

 Label 48.19.l Level $48$ Weight $19$ Character orbit 48.l Rep. character $\chi_{48}(19,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $144$ Sturm bound $152$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$19$$ Character orbit: $$[\chi]$$ $$=$$ 48.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Sturm bound: $$152$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{19}(48, [\chi])$$.

Total New Old
Modular forms 292 144 148
Cusp forms 284 144 140
Eisenstein series 8 0 8

## Trace form

 $$144 q + 339660 q^{4} + 33073908 q^{8} + O(q^{10})$$ $$144 q + 339660 q^{4} + 33073908 q^{8} - 839045016 q^{10} - 5651841760 q^{11} - 12937399704 q^{12} - 73106770844 q^{14} + 99400645152 q^{16} + 43907655420 q^{18} - 498351928608 q^{19} - 2098468750000 q^{20} + 7833863876256 q^{22} + 9677282270080 q^{23} + 4682720095524 q^{24} - 4882357630900 q^{26} + 22710056407560 q^{28} - 9591482456800 q^{29} - 50281167811608 q^{30} + 40961125409440 q^{32} - 8739379185696 q^{34} - 25716202410144 q^{35} - 68987191635252 q^{36} - 55256394434400 q^{37} + 102529881407688 q^{38} + 1070074165009968 q^{40} + 1127091024027540 q^{42} + 578372646474144 q^{43} - 5138983021336616 q^{44} - 191216307787992 q^{46} - 649495465298064 q^{48} + 33498794014157808 q^{49} - 2394852014509916 q^{50} + 3755326832869536 q^{51} - 15407950167714096 q^{52} - 8709279302119840 q^{53} + 1738636226577036 q^{54} + 17404474912061184 q^{55} - 33091239283146464 q^{56} + 29217180917604816 q^{58} + 37364004031220608 q^{59} + 11397917295469368 q^{60} - 17834505241789728 q^{61} - 100228071710679972 q^{62} + 114042098349681768 q^{64} - 32530699926585632 q^{65} - 14264452687853592 q^{66} + 65323777159050048 q^{67} - 68437964356846528 q^{68} + 26342656148137824 q^{69} + 165750019488544896 q^{70} + 197043326551167488 q^{71} + 32309755594394940 q^{72} + 339308754580001292 q^{74} + 180032667478126272 q^{75} + 72346997295660744 q^{76} - 228072201209228320 q^{77} - 219318518510844804 q^{78} + 773262908118305832 q^{80} - 2401514164751985936 q^{81} - 767830743440103240 q^{82} + 627794169141753440 q^{83} + 100219019741670600 q^{84} - 372637439437500000 q^{85} + 2339091014276103504 q^{86} - 1187597832686533152 q^{88} - 92563888647548664 q^{90} + 1260265707567438624 q^{91} + 1111890028259949808 q^{92} - 1358477795096274024 q^{94} - 1215795719662610400 q^{96} - 3281864229816315416 q^{98} - 729879766136606880 q^{99} + O(q^{100})$$

## Decomposition of $$S_{19}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{19}^{\mathrm{old}}(48, [\chi])$$ into lower level spaces

$$S_{19}^{\mathrm{old}}(48, [\chi]) \simeq$$ $$S_{19}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 2}$$