# Properties

 Label 572.2.bf Level $572$ Weight $2$ Character orbit 572.bf Rep. character $\chi_{572}(67,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $280$ 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.bf (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$52$$ 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 352 280 72
Cusp forms 320 280 40
Eisenstein series 32 0 32

## Trace form

 $$280q - 4q^{5} + 12q^{6} - 12q^{8} + 140q^{9} + O(q^{10})$$ $$280q - 4q^{5} + 12q^{6} - 12q^{8} + 140q^{9} - 16q^{14} - 24q^{18} - 16q^{20} + 16q^{21} - 28q^{26} - 40q^{28} - 20q^{32} - 16q^{34} - 36q^{36} - 36q^{37} + 80q^{40} - 40q^{41} + 20q^{42} + 8q^{44} - 40q^{45} + 60q^{46} - 20q^{48} - 144q^{49} + 20q^{50} + 108q^{52} + 8q^{53} + 20q^{54} + 108q^{56} - 64q^{57} + 60q^{58} + 108q^{60} - 20q^{61} - 36q^{62} - 40q^{65} - 40q^{66} - 76q^{68} - 44q^{70} - 20q^{72} - 100q^{73} - 32q^{74} + 32q^{76} - 140q^{78} - 156q^{80} - 140q^{81} - 260q^{84} - 12q^{85} + 56q^{86} - 72q^{88} + 60q^{89} + 80q^{92} + 80q^{93} + 32q^{94} + 80q^{96} + 44q^{97} + 16q^{98} + O(q^{100})$$

## 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.bf.a $$280$$ $$4.567$$ None $$0$$ $$0$$ $$-4$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(572, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 2}$$