# Properties

 Label 672.2.bj Level 672 Weight 2 Character orbit bj Rep. character $$\chi_{672}(95,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 64 Newform subspaces 1 Sturm bound 256 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 672.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$84$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$256$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(672, [\chi])$$.

Total New Old
Modular forms 288 64 224
Cusp forms 224 64 160
Eisenstein series 64 0 64

## Trace form

 $$64q + O(q^{10})$$ $$64q + 16q^{13} + 8q^{21} + 24q^{25} + 8q^{37} + 8q^{45} - 16q^{49} + 32q^{57} - 16q^{61} + 64q^{69} - 24q^{73} - 8q^{81} + 32q^{85} + 16q^{93} - 80q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(672, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
672.2.bj.a $$64$$ $$5.366$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(672, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(672, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database