# Properties

 Label 1386.2.ch Level $1386$ Weight $2$ Character orbit 1386.ch Rep. character $\chi_{1386}(149,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $768$ 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.ch (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$693$$ 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 2368 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

## Trace form

 $$768q - 192q^{4} + 12q^{9} + O(q^{10})$$ $$768q - 192q^{4} + 12q^{9} + 12q^{11} + 12q^{15} - 192q^{16} + 36q^{23} - 96q^{25} + 36q^{26} + 18q^{27} - 84q^{33} - 150q^{35} - 8q^{36} + 20q^{39} + 40q^{42} + 12q^{44} - 64q^{45} - 40q^{51} + 36q^{53} - 12q^{55} + 40q^{57} - 18q^{58} - 8q^{60} + 110q^{63} - 192q^{64} + 48q^{66} - 136q^{69} + 12q^{70} + 40q^{72} - 28q^{75} - 54q^{77} - 80q^{78} - 92q^{81} + 20q^{84} + 24q^{86} - 60q^{89} + 80q^{90} - 54q^{92} + 14q^{93} - 94q^{99} + O(q^{100})$$

## 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

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