# Properties

 Label 84.2.n Level 84 Weight 2 Character orbit n Rep. character $$\chi_{84}(11,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 24 Newform subspaces 1 Sturm bound 32 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 84.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$84$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(84, [\chi])$$.

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

## Trace form

 $$24q - 2q^{4} - 2q^{9} + O(q^{10})$$ $$24q - 2q^{4} - 2q^{9} - 10q^{10} - 12q^{12} - 24q^{13} - 10q^{16} - 10q^{18} - 6q^{21} + 28q^{22} - 14q^{24} - 12q^{25} + 10q^{28} - 14q^{30} + 10q^{33} - 8q^{34} + 44q^{36} - 8q^{37} + 34q^{40} + 38q^{42} - 18q^{45} + 24q^{46} + 8q^{48} + 16q^{52} + 38q^{54} - 4q^{57} + 14q^{58} + 14q^{60} + 4q^{61} - 68q^{64} + 30q^{66} + 36q^{69} - 90q^{70} + 20q^{72} - 24q^{76} - 104q^{78} + 26q^{81} - 68q^{82} - 76q^{84} - 40q^{85} - 34q^{88} - 40q^{90} - 6q^{93} - 24q^{94} - 62q^{96} + 72q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(84, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
84.2.n.a $$24$$ $$0.671$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database