# Properties

 Label 1600.2.bu Level $1600$ Weight $2$ Character orbit 1600.bu Rep. character $\chi_{1600}(81,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $464$ Sturm bound $480$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1600.bu (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$400$$ Character field: $$\Q(\zeta_{20})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1600, [\chi])$$.

Total New Old
Modular forms 1984 496 1488
Cusp forms 1856 464 1392
Eisenstein series 128 32 96

## Trace form

 $$464q + 6q^{3} - 8q^{5} + O(q^{10})$$ $$464q + 6q^{3} - 8q^{5} + 6q^{11} - 6q^{13} + 16q^{15} - 12q^{17} + 6q^{19} + 12q^{21} + 18q^{27} - 6q^{29} - 12q^{31} - 12q^{33} - 44q^{35} - 6q^{37} + 48q^{43} - 12q^{45} + 12q^{47} - 400q^{49} + 4q^{51} - 6q^{53} + 6q^{59} - 6q^{61} - 72q^{63} + 16q^{65} - 30q^{67} - 18q^{69} + 26q^{75} + 36q^{77} + 52q^{79} + 72q^{81} + 46q^{83} + 2q^{85} - 36q^{91} - 4q^{93} + 40q^{95} - 12q^{97} + 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1600, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1600, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1600, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 3}$$