# Properties

 Label 528.2.b Level $528$ Weight $2$ Character orbit 528.b Rep. character $\chi_{528}(65,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $6$ Sturm bound $192$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$528 = 2^{4} \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 528.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$192$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$17$$, $$29$$

## Dimensions

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

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

## Trace form

 $$22q + 2q^{3} + 2q^{9} + O(q^{10})$$ $$22q + 2q^{3} + 2q^{9} + 2q^{15} - 10q^{25} + 8q^{27} + 4q^{31} - 2q^{33} - 4q^{37} + 8q^{45} - 6q^{49} - 4q^{55} + 60q^{67} - 12q^{69} + 4q^{75} - 6q^{81} - 48q^{91} - 24q^{93} - 20q^{97} - 22q^{99} + O(q^{100})$$

## 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.b.a $$2$$ $$4.216$$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-\beta q^{3}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots$$
528.2.b.b $$2$$ $$4.216$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}-\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots$$
528.2.b.c $$2$$ $$4.216$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta )q^{3}-\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots$$
528.2.b.d $$4$$ $$4.216$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots$$
528.2.b.e $$6$$ $$4.216$$ 6.0.7388168.1 None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots$$
528.2.b.f $$6$$ $$4.216$$ 6.0.7388168.1 None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(528, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(132, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(264, [\chi])$$$$^{\oplus 2}$$