# Properties

 Label 360.2.m Level $360$ Weight $2$ Character orbit 360.m Rep. character $\chi_{360}(179,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $3$ Sturm bound $144$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$360 = 2^{3} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 360.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$120$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$144$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(360, [\chi])$$.

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

## Trace form

 $$24q - 4q^{4} + O(q^{10})$$ $$24q - 4q^{4} - 8q^{10} + 20q^{16} + 16q^{19} - 32q^{34} - 28q^{40} - 48q^{46} + 24q^{49} - 28q^{64} + 32q^{70} - 56q^{76} - 8q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(360, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
360.2.m.a $$4$$ $$2.875$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots$$
360.2.m.b $$4$$ $$2.875$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots$$
360.2.m.c $$16$$ $$2.875$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(360, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(360, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$