# Properties

 Label 1386.2.ce Level $1386$ Weight $2$ Character orbit 1386.ce Rep. character $\chi_{1386}(19,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $320$ Sturm bound $576$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.ce (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1386, [\chi])$$.

Total New Old
Modular forms 2432 320 2112
Cusp forms 2176 320 1856
Eisenstein series 256 0 256

## Trace form

 $$320q - 40q^{4} + 12q^{5} - 10q^{7} + O(q^{10})$$ $$320q - 40q^{4} + 12q^{5} - 10q^{7} - 2q^{14} + 40q^{16} - 30q^{17} - 16q^{22} + 8q^{23} - 36q^{25} + 48q^{26} - 10q^{28} + 20q^{29} + 18q^{31} - 70q^{35} + 8q^{37} - 12q^{38} + 30q^{40} - 10q^{44} - 24q^{47} + 18q^{49} - 8q^{53} + 4q^{56} - 8q^{58} + 60q^{59} + 30q^{61} + 80q^{64} + 32q^{67} + 30q^{68} + 34q^{70} + 56q^{71} + 90q^{73} + 20q^{74} + 34q^{77} + 30q^{79} + 18q^{80} + 12q^{82} + 140q^{85} + 26q^{86} + 2q^{88} + 84q^{89} - 22q^{91} - 44q^{92} + 90q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1386, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1386, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$