# Properties

 Label 572.2.bv Level $572$ Weight $2$ Character orbit 572.bv Rep. character $\chi_{572}(41,\cdot)$ Character field $\Q(\zeta_{60})$ Dimension $224$ Newform subspaces $1$ Sturm bound $168$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.bv (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{60})$$ 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 1440 224 1216
Cusp forms 1248 224 1024
Eisenstein series 192 0 192

## Trace form

 $$224q + 28q^{9} + O(q^{10})$$ $$224q + 28q^{9} + 16q^{11} + 10q^{13} - 28q^{15} - 48q^{23} + 24q^{27} + 20q^{29} + 4q^{31} + 60q^{33} + 50q^{35} + 12q^{37} - 40q^{39} + 20q^{41} + 64q^{45} - 62q^{47} + 100q^{53} - 22q^{55} + 12q^{59} - 40q^{61} - 80q^{63} - 44q^{67} - 152q^{71} + 30q^{73} - 120q^{75} + 80q^{79} + 72q^{81} + 90q^{83} - 40q^{85} - 8q^{89} - 36q^{91} - 90q^{93} - 42q^{97} + 144q^{99} + O(q^{100})$$

## 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.bv.a $$224$$ $$4.567$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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