# Properties

 Label 1386.2.j Level $1386$ Weight $2$ Character orbit 1386.j Rep. character $\chi_{1386}(463,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $120$ 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.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1386, [\chi])$$.

Total New Old
Modular forms 592 120 472
Cusp forms 560 120 440
Eisenstein series 32 0 32

## Trace form

 $$120q - 4q^{3} - 60q^{4} + 4q^{5} - 4q^{9} + O(q^{10})$$ $$120q - 4q^{3} - 60q^{4} + 4q^{5} - 4q^{9} - 4q^{11} - 4q^{12} - 8q^{14} + 20q^{15} - 60q^{16} - 8q^{18} + 4q^{20} - 48q^{25} + 8q^{27} - 8q^{30} + 12q^{31} + 8q^{33} + 8q^{36} - 24q^{37} - 40q^{39} + 32q^{41} + 8q^{44} + 40q^{45} + 44q^{47} + 8q^{48} - 60q^{49} + 8q^{50} + 8q^{51} + 8q^{53} - 24q^{54} - 24q^{55} - 8q^{56} + 32q^{57} - 60q^{59} - 16q^{60} - 48q^{62} - 24q^{63} + 120q^{64} - 72q^{65} + 12q^{67} + 16q^{69} + 24q^{71} + 16q^{72} - 8q^{75} - 8q^{77} + 8q^{78} - 8q^{80} + 4q^{81} + 96q^{82} + 32q^{83} - 48q^{85} - 32q^{86} + 8q^{87} + 32q^{89} - 40q^{90} - 4q^{93} + 56q^{95} - 36q^{97} - 20q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(99, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(198, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$