# Properties

 Label 572.2.bq Level $572$ Weight $2$ Character orbit 572.bq Rep. character $\chi_{572}(49,\cdot)$ Character field $\Q(\zeta_{30})$ 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.bq (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{30})$$ 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

 $$112q + 20q^{9} + O(q^{10})$$ $$112q + 20q^{9} - 6q^{11} + 11q^{13} + 30q^{15} + 16q^{17} - 12q^{19} + 6q^{23} + 40q^{25} - 12q^{27} - 5q^{29} + 9q^{33} - 33q^{35} - 45q^{39} - 18q^{41} + 30q^{45} - 16q^{49} + 48q^{51} - 2q^{53} - 20q^{55} - 39q^{59} + 4q^{61} - 102q^{63} - 6q^{65} + 48q^{67} + 34q^{69} + 84q^{71} - 56q^{75} - 22q^{77} - 24q^{79} + 16q^{81} + 60q^{85} - 34q^{87} - 66q^{89} - 41q^{91} + 123q^{93} + 12q^{95} - 15q^{97} + O(q^{100})$$

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

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

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