# Properties

 Label 1386.2.cs Level $1386$ Weight $2$ Character orbit 1386.cs Rep. character $\chi_{1386}(5,\cdot)$ 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.cs (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

 $$768q + 192q^{4} - 12q^{9} + O(q^{10})$$ $$768q + 192q^{4} - 12q^{9} - 12q^{11} - 12q^{15} - 192q^{16} + 16q^{18} + 20q^{21} + 36q^{23} + 96q^{25} + 36q^{26} + 54q^{27} + 90q^{35} - 8q^{36} - 40q^{42} + 12q^{44} + 48q^{45} + 48q^{50} - 44q^{51} - 36q^{53} + 44q^{57} + 18q^{58} - 120q^{59} - 8q^{60} - 30q^{63} + 192q^{64} - 24q^{66} + 12q^{70} + 24q^{72} + 84q^{75} + 42q^{77} - 80q^{78} - 72q^{79} - 28q^{81} + 24q^{85} - 24q^{86} - 288q^{87} + 60q^{89} + 54q^{92} - 2q^{93} + 48q^{98} + 142q^{99} + O(q^{100})$$

## 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

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