# Properties

 Label 572.2.bh Level $572$ Weight $2$ Character orbit 572.bh Rep. character $\chi_{572}(57,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $112$ 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.bh (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{20})$$ 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 720 112 608
Cusp forms 624 112 512
Eisenstein series 96 0 96

## Trace form

 $$112q - 28q^{9} + O(q^{10})$$ $$112q - 28q^{9} + 8q^{11} - 10q^{13} + 4q^{15} - 24q^{27} - 20q^{29} - 16q^{31} - 54q^{33} + 100q^{35} - 12q^{37} + 40q^{39} - 20q^{41} - 4q^{45} - 10q^{47} - 76q^{53} - 20q^{55} + 18q^{59} + 40q^{61} + 80q^{63} + 92q^{67} + 8q^{71} - 30q^{73} - 80q^{79} + 12q^{81} + 40q^{85} + 32q^{89} - 12q^{91} - 114q^{93} + 54q^{97} - 90q^{99} + O(q^{100})$$

## 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.bh.a $$112$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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