Properties

 Label 1386.2.co Level $1386$ Weight $2$ Character orbit 1386.co Rep. character $\chi_{1386}(107,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $256$ 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.co (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$231$$ 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 256 2176
Cusp forms 2176 256 1920
Eisenstein series 256 0 256

Trace form

 $$256q + 32q^{4} + O(q^{10})$$ $$256q + 32q^{4} + 32q^{16} - 8q^{22} - 48q^{25} + 20q^{28} + 12q^{31} + 64q^{34} - 8q^{37} - 20q^{40} - 80q^{49} + 24q^{55} + 4q^{58} - 160q^{61} - 64q^{64} - 64q^{67} - 12q^{70} - 40q^{73} + 32q^{82} + 160q^{85} + 4q^{88} - 40q^{94} + 64q^{97} + O(q^{100})$$

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

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