# Properties

 Label 2240.2.e Level $2240$ Weight $2$ Character orbit 2240.e Rep. character $\chi_{2240}(2239,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $7$ Sturm bound $768$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$768$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2240, [\chi])$$.

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

## Trace form

 $$92q - 92q^{9} + O(q^{10})$$ $$92q - 92q^{9} - 8q^{21} - 4q^{25} + 8q^{29} - 4q^{49} - 24q^{65} + 44q^{81} - 24q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2240, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2240.2.e.a $$4$$ $$17.886$$ $$\Q(\sqrt{2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}+\beta _{2})q^{3}-\beta _{3}q^{5}+(\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
2240.2.e.b $$4$$ $$17.886$$ $$\Q(\sqrt{5}, \sqrt{-7})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots$$
2240.2.e.c $$4$$ $$17.886$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$$
2240.2.e.d $$8$$ $$17.886$$ 8.0.121550625.1 $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots$$
2240.2.e.e $$8$$ $$17.886$$ 8.0.$$\cdots$$.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots$$
2240.2.e.f $$16$$ $$17.886$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{3}-\beta _{10}q^{5}+(-\beta _{6}+\beta _{8})q^{7}+\cdots$$
2240.2.e.g $$48$$ $$17.886$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2240, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1120, [\chi])$$$$^{\oplus 2}$$