# Properties

 Label 165.6.j Level $165$ Weight $6$ Character orbit 165.j Rep. character $\chi_{165}(43,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $120$ Sturm bound $144$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(i)$$ Sturm bound: $$144$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(165, [\chi])$$.

Total New Old
Modular forms 248 120 128
Cusp forms 232 120 112
Eisenstein series 16 0 16

## Trace form

 $$120 q + 88 q^{5} + O(q^{10})$$ $$120 q + 88 q^{5} - 40 q^{11} - 1584 q^{12} + 792 q^{15} - 32240 q^{16} - 13640 q^{20} - 2908 q^{22} + 10208 q^{23} + 13992 q^{25} - 8400 q^{26} - 9680 q^{31} - 15624 q^{33} - 155520 q^{36} - 37048 q^{37} - 74536 q^{38} + 34848 q^{42} - 52800 q^{47} - 50688 q^{48} + 63624 q^{53} + 47480 q^{55} - 401200 q^{56} + 316736 q^{58} - 50688 q^{60} - 91080 q^{66} + 213408 q^{67} + 262112 q^{70} + 143840 q^{71} + 77760 q^{75} + 412584 q^{77} + 151416 q^{78} - 471720 q^{80} - 787320 q^{81} - 313992 q^{82} - 676400 q^{86} - 456956 q^{88} + 990320 q^{91} + 186880 q^{92} + 4752 q^{93} + 77528 q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(165, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{6}^{\mathrm{old}}(165, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(165, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$