# Properties

 Label 1470.2.bt Level $1470$ Weight $2$ Character orbit 1470.bt Rep. character $\chi_{1470}(23,\cdot)$ Character field $\Q(\zeta_{84})$ Dimension $2688$ Sturm bound $672$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.bt (of order $$84$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$735$$ Character field: $$\Q(\zeta_{84})$$ Sturm bound: $$672$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1470, [\chi])$$.

Total New Old
Modular forms 8256 2688 5568
Cusp forms 7872 2688 5184
Eisenstein series 384 0 384

## Trace form

 $$2688q + 20q^{6} - 4q^{7} + O(q^{10})$$ $$2688q + 20q^{6} - 4q^{7} - 4q^{10} + 24q^{15} - 224q^{16} - 12q^{21} - 20q^{22} + 72q^{27} - 4q^{28} + 12q^{30} - 32q^{31} + 20q^{33} - 20q^{36} - 72q^{42} + 64q^{43} + 140q^{45} + 312q^{46} + 16q^{55} - 92q^{57} + 224q^{58} + 200q^{61} + 88q^{63} + 16q^{67} + 40q^{70} + 56q^{73} - 92q^{75} + 32q^{76} + 32q^{81} - 16q^{82} - 48q^{85} - 76q^{87} - 4q^{88} - 124q^{90} - 176q^{91} + 88q^{93} - 4q^{96} - 104q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1470, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1470, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1470, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(735, [\chi])$$$$^{\oplus 2}$$