# Properties

 Label 240.2.t Level $240$ Weight $2$ Character orbit 240.t Rep. character $\chi_{240}(59,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.t (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$240$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(240, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88q - 8q^{4} - 4q^{6} + O(q^{10})$$ $$88q - 8q^{4} - 4q^{6} - 4q^{10} - 4q^{16} + 8q^{21} - 20q^{24} + 8q^{30} - 60q^{34} - 28q^{36} - 8q^{39} - 8q^{40} - 12q^{45} - 52q^{46} - 56q^{49} - 16q^{51} + 24q^{54} - 40q^{55} + 40q^{60} + 8q^{61} - 32q^{64} - 56q^{66} - 16q^{69} + 48q^{70} - 36q^{75} - 76q^{76} - 8q^{81} + 128q^{84} - 24q^{85} + 72q^{90} + 48q^{91} + 52q^{94} - 24q^{96} - 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(240, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
240.2.t.a $$8$$ $$1.916$$ 8.0.3317760000.5 $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$$
240.2.t.b $$80$$ $$1.916$$ None $$0$$ $$0$$ $$0$$ $$0$$