# Properties

 Label 693.2.bj Level 693 Weight 2 Character orbit bj Rep. character $$\chi_{693}(76,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 184 Newform subspaces 1 Sturm bound 192 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$693 = 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 693.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$693$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(693, [\chi])$$.

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

## Trace form

 $$184q + 84q^{4} + O(q^{10})$$ $$184q + 84q^{4} - 10q^{14} - 24q^{15} - 76q^{16} - 10q^{22} - 16q^{23} + 72q^{25} - 24q^{36} - 16q^{37} + 10q^{42} + 60q^{44} - 2q^{49} + 32q^{53} + 40q^{56} - 44q^{58} - 120q^{60} - 128q^{64} - 4q^{67} - 20q^{70} + 16q^{71} - 4q^{77} + 68q^{78} - 8q^{81} - 12q^{86} + 34q^{88} + 20q^{91} + 64q^{92} - 32q^{93} - 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(693, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
693.2.bj.a $$184$$ $$5.534$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database