# Properties

 Label 861.2.l Level 861 Weight 2 Character orbit l Rep. character $$\chi_{861}(419,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 216 Newforms 1 Sturm bound 224 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$861 = 3 \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 861.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$861$$ Character field: $$\Q(i)$$ Newforms: $$1$$ Sturm bound: $$224$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(861, [\chi])$$.

Total New Old
Modular forms 232 232 0
Cusp forms 216 216 0
Eisenstein series 16 16 0

## Trace form

 $$216q + 192q^{4} - 4q^{7} + O(q^{10})$$ $$216q + 192q^{4} - 4q^{7} + 20q^{15} + 144q^{16} - 24q^{18} - 56q^{22} - 200q^{25} - 40q^{28} + 32q^{30} + 16q^{37} + 4q^{42} - 16q^{51} - 64q^{57} - 32q^{58} + 40q^{60} - 6q^{63} + 48q^{64} - 48q^{67} + 48q^{70} - 92q^{72} + 28q^{78} + 8q^{79} - 120q^{81} + 16q^{85} - 144q^{88} - 16q^{93} + 56q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(861, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
861.2.l.a $$216$$ $$6.875$$ None $$0$$ $$0$$ $$0$$ $$-4$$