# Properties

 Label 165.6.w Level $165$ Weight $6$ Character orbit 165.w Rep. character $\chi_{165}(7,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $480$ Sturm bound $144$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.w (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ Sturm bound: $$144$$

## Dimensions

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

Total New Old
Modular forms 992 480 512
Cusp forms 928 480 448
Eisenstein series 64 0 64

## Trace form

 $$480 q - 88 q^{5} + 1180 q^{7} + O(q^{10})$$ $$480 q - 88 q^{5} + 1180 q^{7} + 40 q^{11} + 1584 q^{12} + 1188 q^{15} + 32240 q^{16} - 3820 q^{17} - 20460 q^{20} + 2908 q^{22} - 10208 q^{23} - 1232 q^{25} + 8400 q^{26} + 18240 q^{28} - 6840 q^{30} + 9680 q^{31} + 15624 q^{33} + 155520 q^{36} + 37048 q^{37} + 74536 q^{38} - 144600 q^{41} + 52272 q^{42} - 334000 q^{46} - 85140 q^{47} - 76032 q^{48} + 28480 q^{50} + 52200 q^{51} - 28360 q^{52} + 95436 q^{53} + 66960 q^{55} + 533600 q^{56} + 71640 q^{57} - 300016 q^{58} - 76032 q^{60} - 113800 q^{61} - 317120 q^{62} - 95580 q^{63} - 45720 q^{66} - 509488 q^{67} + 244480 q^{68} + 235088 q^{70} - 143840 q^{71} - 49260 q^{73} - 77760 q^{75} - 412584 q^{77} + 605664 q^{78} - 91480 q^{80} + 787320 q^{81} - 452048 q^{82} - 632200 q^{83} + 549520 q^{85} + 676400 q^{86} + 157716 q^{88} + 1880 q^{91} + 1035220 q^{92} + 7128 q^{93} - 1402740 q^{95} - 1488608 q^{97} + O(q^{100})$$

## 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

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