# Properties

 Label 2280.2.j Level $2280$ Weight $2$ Character orbit 2280.j Rep. character $\chi_{2280}(1369,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $9$ Sturm bound $960$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2280.j (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$960$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2280, [\chi])$$.

Total New Old
Modular forms 496 56 440
Cusp forms 464 56 408
Eisenstein series 32 0 32

## Trace form

 $$56q - 8q^{5} - 56q^{9} + O(q^{10})$$ $$56q - 8q^{5} - 56q^{9} - 4q^{15} + 12q^{19} - 4q^{25} + 32q^{29} - 12q^{35} + 8q^{39} - 32q^{41} + 8q^{45} - 48q^{49} - 12q^{55} - 8q^{61} - 8q^{65} - 16q^{75} + 56q^{81} + 28q^{85} + 48q^{89} + 32q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2280, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2280.2.j.a $$2$$ $$18.206$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2+i)q^{5}+4iq^{7}-q^{9}+\cdots$$
2280.2.j.b $$2$$ $$18.206$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots$$
2280.2.j.c $$2$$ $$18.206$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots$$
2280.2.j.d $$2$$ $$18.206$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots$$
2280.2.j.e $$2$$ $$18.206$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots$$
2280.2.j.f $$6$$ $$18.206$$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
2280.2.j.g $$10$$ $$18.206$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{6}q^{3}+(1-\beta _{2}-\beta _{4})q^{5}+(\beta _{6}+\beta _{9})q^{7}+\cdots$$
2280.2.j.h $$12$$ $$18.206$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}-q^{9}-\beta _{8}q^{11}+\cdots$$
2280.2.j.i $$18$$ $$18.206$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1140, [\chi])$$$$^{\oplus 2}$$