# Properties

 Label 2268.2.l Level $2268$ Weight $2$ Character orbit 2268.l Rep. character $\chi_{2268}(109,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $64$ Newform subspaces $14$ Sturm bound $864$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$864$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$13$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2268, [\chi])$$.

Total New Old
Modular forms 936 64 872
Cusp forms 792 64 728
Eisenstein series 144 0 144

## Trace form

 $$64q - 5q^{7} + O(q^{10})$$ $$64q - 5q^{7} + 5q^{13} - 10q^{19} + 64q^{25} - 10q^{31} + 5q^{37} - 10q^{43} + 19q^{49} + 60q^{55} + 11q^{61} - q^{67} + 2q^{73} - 13q^{79} + 12q^{85} + 11q^{91} + 5q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2268, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2268.2.l.a $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-6$$ $$5$$ $$q-3q^{5}+(2+\zeta_{6})q^{7}+3q^{11}+(-2+\cdots)q^{13}+\cdots$$
2268.2.l.b $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$-5$$ $$q-2q^{5}+(-3+\zeta_{6})q^{7}+2q^{11}+(3+\cdots)q^{13}+\cdots$$
2268.2.l.c $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-1-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots$$
2268.2.l.d $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-2+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{13}+\cdots$$
2268.2.l.e $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{13}+\zeta_{6}q^{19}+\cdots$$
2268.2.l.f $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$5$$ $$q+(2+\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}-8\zeta_{6}q^{19}+\cdots$$
2268.2.l.g $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$4$$ $$-5$$ $$q+2q^{5}+(-3+\zeta_{6})q^{7}-2q^{11}+(3+\cdots)q^{13}+\cdots$$
2268.2.l.h $$2$$ $$18.110$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$5$$ $$q+3q^{5}+(2+\zeta_{6})q^{7}-3q^{11}+(-2+\cdots)q^{13}+\cdots$$
2268.2.l.i $$4$$ $$18.110$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{3}q^{5}+(3+2\beta _{2})q^{7}+2\beta _{3}q^{11}+\cdots$$
2268.2.l.j $$6$$ $$18.110$$ 6.0.309123.1 None $$0$$ $$0$$ $$-2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1})q^{7}+\cdots$$
2268.2.l.k $$6$$ $$18.110$$ 6.0.309123.1 None $$0$$ $$0$$ $$2$$ $$-4$$ $$q+(1-\beta _{1}+\beta _{3})q^{5}+(-1-\beta _{3})q^{7}+\cdots$$
2268.2.l.l $$8$$ $$18.110$$ 8.0.310217769.2 None $$0$$ $$0$$ $$-4$$ $$-2$$ $$q+(-1-\beta _{6})q^{5}+(\beta _{3}+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{11}+\cdots$$
2268.2.l.m $$8$$ $$18.110$$ 8.0.310217769.2 None $$0$$ $$0$$ $$4$$ $$-2$$ $$q+(1+\beta _{6})q^{5}+\beta _{7}q^{7}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots$$
2268.2.l.n $$16$$ $$18.110$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{15}q^{5}+(-1+\beta _{1}-\beta _{4})q^{7}-\beta _{11}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2268, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2268, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(567, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1134, [\chi])$$$$^{\oplus 2}$$