# Properties

 Label 48.19.i Level $48$ Weight $19$ Character orbit 48.i Rep. character $\chi_{48}(5,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $284$ Sturm bound $152$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$19$$ Character orbit: $$[\chi]$$ $$=$$ 48.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ 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 292 292 0
Cusp forms 284 284 0
Eisenstein series 8 8 0

## Trace form

 $$284 q - 2 q^{3} - 4 q^{4} - 13365572 q^{6} + O(q^{10})$$ $$284 q - 2 q^{3} - 4 q^{4} - 13365572 q^{6} + 1335937496 q^{10} - 12012956672 q^{12} - 4 q^{13} - 4 q^{15} + 168768284144 q^{16} + 544202860260 q^{18} - 498351928612 q^{19} + 774840976 q^{21} - 1310509027048 q^{22} + 788418910792 q^{24} - 14062217323442 q^{27} + 14904250085880 q^{28} - 77759171687196 q^{30} - 8 q^{31} - 4 q^{33} + 159416196148008 q^{34} + 598380050125060 q^{36} - 4 q^{37} - 1543178393880232 q^{40} + 543960577097080 q^{42} + 833812222297532 q^{43} - 7629394531252 q^{45} + 3580309118862136 q^{46} - 5391222456721808 q^{48} - 60483933636673828 q^{49} - 6279971520088224 q^{51} - 8222225871647488 q^{52} + 7787112123537640 q^{54} + 1578077176502840 q^{58} + 3769549073101824 q^{60} - 17834505241789732 q^{61} + 6513654391641792 q^{63} - 37336792379767528 q^{64} + 62959391314171924 q^{66} - 105732829263162244 q^{67} - 774840980 q^{69} - 70653025186507368 q^{70} - 83730200639517240 q^{72} - 216814920711427022 q^{75} - 258754732464415288 q^{76} - 354793625136195028 q^{78} + 478283655785842936 q^{79} - 4 q^{81} - 465014738882769920 q^{82} - 816775326597917072 q^{84} + 372652698226562496 q^{85} + 136258368541812320 q^{88} - 1465228519901203152 q^{90} - 668969173550359008 q^{91} - 1244353835466496580 q^{93} + 31417741085559408 q^{94} - 1005542260323039256 q^{96} - 8 q^{97} + 1141285608651415004 q^{99} + O(q^{100})$$

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

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