# Properties

 Label 572.2.bc Level $572$ Weight $2$ Character orbit 572.bc Rep. character $\chi_{572}(197,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $56$ 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.bc (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{12})$$ 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 360 56 304
Cusp forms 312 56 256
Eisenstein series 48 0 48

## Trace form

 $$56q - 28q^{9} + O(q^{10})$$ $$56q - 28q^{9} + 4q^{11} + 8q^{15} - 12q^{23} - 24q^{27} - 4q^{31} - 10q^{33} - 12q^{37} - 64q^{45} - 8q^{47} + 40q^{53} + 22q^{55} + 48q^{59} - 36q^{67} - 48q^{71} + 120q^{75} + 28q^{81} + 28q^{89} + 36q^{91} + 20q^{93} - 68q^{97} - 44q^{99} + O(q^{100})$$

## 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.bc.a $$56$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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