# Properties

 Label 1386.2.cf Level $1386$ Weight $2$ Character orbit 1386.cf Rep. character $\chi_{1386}(29,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $576$ 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.cf (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$99$$ 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 576 1792
Cusp forms 2240 576 1664
Eisenstein series 128 0 128

## Trace form

 $$576q + 8q^{3} + 72q^{4} + 12q^{5} - 10q^{6} + 16q^{9} + O(q^{10})$$ $$576q + 8q^{3} + 72q^{4} + 12q^{5} - 10q^{6} + 16q^{9} + 18q^{11} - 24q^{12} + 72q^{16} + 20q^{18} - 60q^{19} - 12q^{20} - 6q^{22} + 10q^{24} - 60q^{25} + 32q^{27} + 180q^{29} + 60q^{30} - 12q^{31} - 4q^{33} - 12q^{34} + 22q^{36} + 24q^{37} + 120q^{38} + 100q^{39} + 48q^{45} - 12q^{47} - 4q^{48} - 72q^{49} - 10q^{51} + 20q^{57} + 114q^{59} + 8q^{60} - 144q^{64} - 32q^{66} + 60q^{67} + 40q^{69} + 50q^{75} + 128q^{78} - 104q^{81} + 36q^{82} - 180q^{83} - 40q^{84} - 102q^{86} - 6q^{88} - 200q^{90} + 72q^{91} - 176q^{93} - 240q^{95} + 30q^{97} + 220q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(198, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$