# Properties

 Label 1380.2.p Level $1380$ Weight $2$ Character orbit 1380.p Rep. character $\chi_{1380}(91,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $2$ Sturm bound $576$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1380.p (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$10$$

## Dimensions

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

Total New Old
Modular forms 296 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

## Trace form

 $$96q - 8q^{2} - 4q^{4} - 4q^{6} - 8q^{8} - 96q^{9} + O(q^{10})$$ $$96q - 8q^{2} - 4q^{4} - 4q^{6} - 8q^{8} - 96q^{9} - 12q^{16} + 8q^{18} + 4q^{24} - 96q^{25} - 40q^{26} + 64q^{29} + 32q^{32} + 4q^{36} - 16q^{41} + 40q^{46} + 32q^{48} + 80q^{49} + 8q^{50} - 32q^{52} + 4q^{54} - 16q^{58} + 48q^{62} - 52q^{64} - 16q^{69} + 8q^{72} + 64q^{77} + 96q^{81} - 40q^{82} + 32q^{85} - 32q^{92} - 64q^{94} - 4q^{96} + 48q^{98} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1380.2.p.a $$48$$ $$11.019$$ None $$-4$$ $$0$$ $$0$$ $$0$$
1380.2.p.b $$48$$ $$11.019$$ None $$-4$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1380, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(276, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 2}$$