# Properties

 Label 2016.2.dq Level 2016 Weight 2 Character orbit dq Rep. character $$\chi_{2016}(307,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 632 Sturm bound 768

# Related objects

## Defining parameters

 Level: $$N$$ = $$2016 = 2^{5} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2016.dq (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$224$$ Character field: $$\Q(\zeta_{8})$$ Sturm bound: $$768$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2016, [\chi])$$.

Total New Old
Modular forms 1568 648 920
Cusp forms 1504 632 872
Eisenstein series 64 16 48

## Trace form

 $$632q + 8q^{2} - 8q^{4} - 4q^{7} + 8q^{8} + O(q^{10})$$ $$632q + 8q^{2} - 8q^{4} - 4q^{7} + 8q^{8} + 8q^{11} - 12q^{14} - 4q^{16} - 4q^{22} - 8q^{25} - 24q^{28} + 8q^{29} + 8q^{32} + 28q^{35} - 8q^{37} - 16q^{43} + 100q^{44} - 8q^{46} + 32q^{50} + 24q^{53} - 36q^{56} + 56q^{58} - 80q^{64} + 16q^{65} - 16q^{67} - 40q^{70} + 72q^{71} - 108q^{74} + 4q^{77} - 16q^{79} - 48q^{85} + 8q^{86} - 96q^{88} + 44q^{91} + 84q^{92} - 56q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2016, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(2016, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2016, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database