# Properties

 Label 1380.2.bs Level $1380$ Weight $2$ Character orbit 1380.bs Rep. character $\chi_{1380}(37,\cdot)$ Character field $\Q(\zeta_{44})$ Dimension $480$ Sturm bound $576$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1380.bs (of order $$44$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q(\zeta_{44})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1380, [\chi])$$.

Total New Old
Modular forms 6000 480 5520
Cusp forms 5520 480 5040
Eisenstein series 480 0 480

## Trace form

 $$480q + O(q^{10})$$ $$480q + 8q^{13} - 72q^{23} + 8q^{25} - 8q^{31} - 8q^{35} + 88q^{37} + 24q^{41} + 168q^{47} + 32q^{55} + 88q^{57} - 88q^{61} + 24q^{71} - 8q^{73} - 32q^{75} - 40q^{77} + 48q^{81} + 64q^{85} + 40q^{87} + 220q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1380, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1380, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1380, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(345, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(690, [\chi])$$$$^{\oplus 2}$$