# Properties

 Label 2816.2.g Level $2816$ Weight $2$ Character orbit 2816.g Rep. character $\chi_{2816}(1407,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $9$ Sturm bound $768$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2816 = 2^{8} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2816.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$88$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$768$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2816, [\chi])$$.

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

## Trace form

 $$92 q + 92 q^{9} + O(q^{10})$$ $$92 q + 92 q^{9} - 68 q^{25} + 8 q^{33} + 60 q^{49} + 76 q^{81} + 8 q^{89} - 8 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2816, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2816.2.g.a $4$ $22.486$ $$\Q(i, \sqrt{11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-3\beta _{1}q^{5}+8q^{9}+\beta _{2}q^{11}+\cdots$$
2816.2.g.b $8$ $22.486$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{4}q^{3}+\zeta_{24}q^{5}+\zeta_{24}^{6}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots$$
2816.2.g.c $8$ $22.486$ 8.0.303595776.1 $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(1+\beta _{5}+\cdots)q^{9}+\cdots$$
2816.2.g.d $12$ $22.486$ 12.0.$$\cdots$$.1 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(-1+\beta _{8})q^{3}+\beta _{4}q^{5}+\beta _{11}q^{7}+\cdots$$
2816.2.g.e $12$ $22.486$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$-8$$ $$q-\beta _{3}q^{3}+\beta _{7}q^{5}+(-1-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots$$
2816.2.g.f $12$ $22.486$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$8$$ $$q-\beta _{3}q^{3}-\beta _{7}q^{5}+(1+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$$
2816.2.g.g $12$ $22.486$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$-8$$ $$q+\beta _{3}q^{3}+\beta _{7}q^{5}+(-1-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots$$
2816.2.g.h $12$ $22.486$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\beta _{3}q^{3}+\beta _{7}q^{5}+(1+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$$
2816.2.g.i $12$ $22.486$ 12.0.$$\cdots$$.1 None $$0$$ $$8$$ $$0$$ $$0$$ $$q+(1-\beta _{8})q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(1+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2816, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2816, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(176, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(352, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(704, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1408, [\chi])$$$$^{\oplus 2}$$