# Properties

 Label 240.2.bk Level $240$ Weight $2$ Character orbit 240.bk Rep. character $\chi_{240}(11,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $64$ 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.bk (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ 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 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

## Trace form

 $$64q + 12q^{6} + O(q^{10})$$ $$64q + 12q^{6} - 4q^{10} + 12q^{12} - 36q^{16} - 20q^{18} + 8q^{19} - 24q^{22} - 36q^{24} - 24q^{27} - 24q^{28} - 4q^{34} + 12q^{36} - 48q^{39} + 20q^{42} + 60q^{46} + 40q^{48} + 64q^{49} - 40q^{51} + 8q^{52} + 72q^{54} - 104q^{58} + 28q^{60} - 16q^{61} - 96q^{64} + 24q^{66} - 64q^{67} - 56q^{72} + 4q^{76} - 40q^{78} - 32q^{82} - 16q^{84} - 16q^{85} + 8q^{88} + 36q^{90} + 48q^{91} - 48q^{93} + 28q^{94} + 88q^{96} + 32q^{99} + O(q^{100})$$

## 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.bk.a $$4$$ $$1.916$$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$-16$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$$
240.2.bk.b $$60$$ $$1.916$$ None $$0$$ $$4$$ $$0$$ $$16$$

## Decomposition of $$S_{2}^{\mathrm{old}}(240, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$