# Properties

 Label 528.2.o Level $528$ Weight $2$ Character orbit 528.o Rep. character $\chi_{528}(175,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $2$ Sturm bound $192$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$528 = 2^{4} \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 528.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$44$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(528, [\chi])$$.

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

## Trace form

 $$12 q - 12 q^{9} + O(q^{10})$$ $$12 q - 12 q^{9} - 12 q^{25} - 12 q^{33} + 84 q^{49} - 48 q^{53} - 48 q^{77} + 12 q^{81} + 24 q^{89} - 48 q^{93} + 48 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(528, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.2.o.a $4$ $4.216$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\beta _{1}q^{3}-2q^{5}-\beta _{3}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
528.2.o.b $8$ $4.216$ 8.0.454201344.7 None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-\beta _{7}q^{7}-q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(528, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(528, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(132, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(176, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(264, [\chi])$$$$^{\oplus 2}$$