# Properties

 Label 2240.2.b Level $2240$ Weight $2$ Character orbit 2240.b Rep. character $\chi_{2240}(1121,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $8$ Sturm bound $768$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$768$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$23$$, $$31$$

## Dimensions

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

Total New Old
Modular forms 408 48 360
Cusp forms 360 48 312
Eisenstein series 48 0 48

## Trace form

 $$48q - 48q^{9} + O(q^{10})$$ $$48q - 48q^{9} - 48q^{25} + 96q^{33} - 96q^{41} + 48q^{49} - 96q^{57} + 144q^{81} + O(q^{100})$$

## 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.b.a $$2$$ $$17.886$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{5}-q^{7}+3q^{9}-2iq^{11}-2iq^{13}+\cdots$$
2240.2.b.b $$2$$ $$17.886$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{5}+q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots$$
2240.2.b.c $$4$$ $$17.886$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}-\zeta_{12}q^{11}+\cdots$$
2240.2.b.d $$4$$ $$17.886$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+q^{7}+\zeta_{12}q^{11}+\cdots$$
2240.2.b.e $$6$$ $$17.886$$ 6.0.3534400.1 None $$0$$ $$0$$ $$0$$ $$-6$$ $$q-\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots$$
2240.2.b.f $$6$$ $$17.886$$ 6.0.3534400.1 None $$0$$ $$0$$ $$0$$ $$6$$ $$q-\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots$$
2240.2.b.g $$12$$ $$17.886$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q-\beta _{11}q^{3}+\beta _{9}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$$
2240.2.b.h $$12$$ $$17.886$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q-\beta _{11}q^{3}-\beta _{9}q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(2240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1120, [\chi])$$$$^{\oplus 2}$$