# Properties

 Label 48.4.k Level $48$ Weight $4$ Character orbit 48.k Rep. character $\chi_{48}(11,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $44$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 48.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(48, [\chi])$$.

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

## Trace form

 $$44q - 2q^{3} - 4q^{4} + 28q^{6} - 8q^{7} + O(q^{10})$$ $$44q - 2q^{3} - 4q^{4} + 28q^{6} - 8q^{7} + 56q^{10} - 80q^{12} - 4q^{13} - 112q^{16} + 52q^{18} + 20q^{19} - 56q^{21} - 40q^{22} - 120q^{24} - 134q^{27} - 296q^{28} - 332q^{30} - 4q^{33} + 520q^{34} - 604q^{36} - 4q^{37} + 596q^{39} + 632q^{40} + 696q^{42} - 436q^{43} - 252q^{45} + 664q^{46} + 1200q^{48} + 972q^{49} - 648q^{51} + 320q^{52} + 1592q^{54} + 280q^{55} - 424q^{58} + 800q^{60} - 916q^{61} - 2056q^{64} - 668q^{66} - 1636q^{67} + 52q^{69} - 5192q^{70} - 3704q^{72} + 1454q^{75} - 568q^{76} - 4932q^{78} - 4q^{81} + 768q^{82} - 2096q^{84} + 736q^{85} + 1284q^{87} + 8864q^{88} + 2672q^{90} + 424q^{91} - 2084q^{93} + 5616q^{94} + 8008q^{96} - 8q^{97} + 1196q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
48.4.k.a $$44$$ $$2.832$$ None $$0$$ $$-2$$ $$0$$ $$-8$$