# Properties

 Label 252.2.ba Level 252 Weight 2 Character orbit ba Rep. character $$\chi_{252}(155,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 72 Newform subspaces 1 Sturm bound 96 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 252.ba (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(252, [\chi])$$.

Total New Old
Modular forms 104 72 32
Cusp forms 88 72 16
Eisenstein series 16 0 16

## Trace form

 $$72q + 6q^{6} + 4q^{9} + O(q^{10})$$ $$72q + 6q^{6} + 4q^{9} - 12q^{12} - 34q^{18} - 42q^{20} - 2q^{24} + 36q^{25} + 28q^{30} + 30q^{32} - 44q^{33} - 12q^{34} + 20q^{36} - 12q^{40} - 60q^{41} + 20q^{42} - 24q^{45} - 24q^{46} - 28q^{48} + 36q^{49} - 78q^{50} - 18q^{52} - 10q^{54} - 4q^{57} - 18q^{58} - 76q^{60} - 60q^{64} + 24q^{65} + 54q^{66} + 78q^{68} + 24q^{69} + 74q^{72} - 24q^{73} + 12q^{76} - 20q^{78} - 4q^{81} - 36q^{82} + 14q^{84} + 30q^{86} + 24q^{88} + 8q^{90} - 114q^{92} - 96q^{93} + 42q^{94} + 112q^{96} - 12q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.2.ba.a $$72$$ $$2.012$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database