# Properties

 Label 572.2.m Level $572$ Weight $2$ Character orbit 572.m Rep. character $\chi_{572}(21,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $28$ Newform subspaces $1$ Sturm bound $168$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$168$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(572, [\chi])$$.

Total New Old
Modular forms 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

## Trace form

 $$28q + 28q^{9} + O(q^{10})$$ $$28q + 28q^{9} + 2q^{11} + 16q^{15} + 24q^{27} + 16q^{31} + 4q^{33} + 12q^{37} + 4q^{45} + 20q^{47} - 64q^{53} + 20q^{55} + 12q^{59} - 12q^{67} - 48q^{71} - 52q^{81} - 52q^{89} + 12q^{91} + 4q^{93} + 56q^{97} - 10q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(572, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
572.2.m.a $$28$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(572, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(572, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(286, [\chi])$$$$^{\oplus 2}$$