# Properties

 Label 756.2.bp Level 756 Weight 2 Character orbit bp Rep. character $$\chi_{756}(193,\cdot)$$ Character field $$\Q(\zeta_{9})$$ Dimension 144 Newform subspaces 1 Sturm bound 288 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$756 = 2^{2} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 756.bp (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$1$$ Sturm bound: $$288$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(756, [\chi])$$.

Total New Old
Modular forms 900 144 756
Cusp forms 828 144 684
Eisenstein series 72 0 72

## Trace form

 $$144q - 12q^{9} + O(q^{10})$$ $$144q - 12q^{9} - 12q^{11} - 12q^{15} - 24q^{17} - 3q^{21} + 15q^{23} + 6q^{29} + 18q^{33} + 18q^{35} + 18q^{39} - 12q^{41} + 6q^{45} + 18q^{47} + 36q^{49} + 18q^{51} + 15q^{53} + 3q^{57} + 30q^{59} + 18q^{61} + 3q^{63} + 9q^{65} + 30q^{69} - 12q^{71} - 36q^{73} + 102q^{75} + 69q^{77} + 18q^{79} + 12q^{81} - 36q^{85} + 78q^{87} - 72q^{89} - 18q^{91} - 60q^{93} + 42q^{95} - 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(756, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
756.2.bp.a $$144$$ $$6.037$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(756, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(756, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database