# Properties

 Label 1386.2.cj Level $1386$ Weight $2$ Character orbit 1386.cj Rep. character $\chi_{1386}(13,\cdot)$ 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.cj (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

 $$768q - 96q^{4} - 24q^{9} + O(q^{10})$$ $$768q - 96q^{4} - 24q^{9} + 4q^{11} + 12q^{15} + 96q^{16} - 24q^{23} - 96q^{25} + 100q^{35} + 8q^{36} - 40q^{39} + 44q^{42} + 8q^{44} - 20q^{51} + 208q^{53} - 80q^{57} + 36q^{58} + 8q^{60} + 10q^{63} + 192q^{64} + 12q^{70} - 112q^{71} - 40q^{72} - 6q^{77} + 96q^{78} - 56q^{81} - 20q^{84} + 8q^{86} - 36q^{92} - 12q^{93} + 80q^{95} - 336q^{99} + O(q^{100})$$

## 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

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