# Properties

 Label 240.2.y Level $240$ Weight $2$ Character orbit 240.y Rep. character $\chi_{240}(163,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $48$ Newform subspaces $6$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.y (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 104 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

## Trace form

 $$48q - 4q^{4} + 12q^{8} + 48q^{9} + O(q^{10})$$ $$48q - 4q^{4} + 12q^{8} + 48q^{9} - 8q^{12} + 4q^{16} + 8q^{19} + 12q^{20} - 28q^{22} - 28q^{28} - 24q^{30} - 20q^{32} - 20q^{34} - 24q^{35} - 4q^{36} - 16q^{38} - 68q^{40} - 20q^{42} + 48q^{44} - 4q^{46} - 48q^{47} - 16q^{48} + 8q^{50} - 8q^{51} + 8q^{52} - 48q^{56} - 68q^{58} - 32q^{59} - 16q^{61} + 16q^{62} - 4q^{64} - 24q^{66} + 72q^{68} + 16q^{69} + 76q^{70} - 64q^{71} + 12q^{72} + 16q^{73} + 32q^{74} + 16q^{75} + 28q^{76} + 24q^{78} + 12q^{80} + 48q^{81} - 80q^{83} - 24q^{84} + 48q^{86} + 28q^{88} - 32q^{91} + 96q^{92} + 28q^{94} - 80q^{95} + 112q^{98} + O(q^{100})$$

## 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.y.a $$2$$ $$1.916$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots$$
240.2.y.b $$2$$ $$1.916$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$2$$ $$-2$$ $$6$$ $$q+(-1-i)q^{2}+q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots$$
240.2.y.c $$2$$ $$1.916$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$-2$$ $$2$$ $$6$$ $$q+(1+i)q^{2}-q^{3}+2iq^{4}+(1-2i)q^{5}+\cdots$$
240.2.y.d $$6$$ $$1.916$$ 6.0.399424.1 None $$0$$ $$6$$ $$6$$ $$-2$$ $$q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$$
240.2.y.e $$16$$ $$1.916$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$2$$ $$16$$ $$-4$$ $$-4$$ $$q+\beta _{7}q^{2}+q^{3}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$$
240.2.y.f $$20$$ $$1.916$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$-20$$ $$0$$ $$-4$$ $$q+\beta _{13}q^{2}-q^{3}-\beta _{3}q^{4}+\beta _{7}q^{5}-\beta _{13}q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$