# Properties

 Label 48.3.i Level $48$ Weight $3$ Character orbit 48.i Rep. character $\chi_{48}(5,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $28$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 48.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(48, [\chi])$$.

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

## Trace form

 $$28q - 2q^{3} - 4q^{4} + 4q^{6} + O(q^{10})$$ $$28q - 2q^{3} - 4q^{4} + 4q^{6} - 24q^{10} - 32q^{12} - 4q^{13} - 4q^{15} - 16q^{16} - 60q^{18} - 36q^{19} + 16q^{21} + 40q^{22} - 56q^{24} - 50q^{27} + 120q^{28} + 84q^{30} - 8q^{31} - 4q^{33} + 136q^{34} + 196q^{36} - 4q^{37} + 88q^{40} + 280q^{42} - 68q^{43} - 52q^{45} - 200q^{46} + 112q^{48} - 36q^{49} + 96q^{51} - 320q^{52} - 128q^{54} - 568q^{58} - 576q^{60} - 36q^{61} + 192q^{63} - 232q^{64} - 572q^{66} + 124q^{67} - 20q^{69} + 312q^{70} - 312q^{72} + 178q^{75} + 776q^{76} + 236q^{78} + 248q^{79} - 4q^{81} + 736q^{82} + 880q^{84} - 64q^{85} + 352q^{88} + 1008q^{90} + 288q^{91} - 68q^{93} - 336q^{94} + 488q^{96} - 8q^{97} - 292q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
48.3.i.a $$8$$ $$1.308$$ 8.0.629407744.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$$
48.3.i.b $$20$$ $$1.308$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots$$