# Properties

 Label 672.2.bu Level 672 Weight 2 Character orbit bu Rep. character $$\chi_{672}(139,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 256 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.bu (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$224$$ Character field: $$\Q(\zeta_{8})$$ 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 528 256 272
Cusp forms 496 256 240
Eisenstein series 32 0 32

## Trace form

 $$256q + O(q^{10})$$ $$256q + 32q^{14} - 8q^{16} + 8q^{18} - 8q^{22} + 16q^{23} + 40q^{28} - 48q^{35} + 16q^{43} - 8q^{44} - 48q^{50} - 32q^{53} + 64q^{58} + 48q^{60} - 144q^{64} + 16q^{67} + 72q^{70} - 128q^{71} + 232q^{74} - 48q^{78} + 176q^{88} + 48q^{91} - 152q^{92} - 32q^{98} + O(q^{100})$$

## 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.bu.a $$256$$ $$5.366$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(672, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database