# Properties

 Label 165.6.v Level $165$ Weight $6$ Character orbit 165.v Rep. character $\chi_{165}(38,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $928$ Sturm bound $144$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.v (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ 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 992 992 0
Cusp forms 928 928 0
Eisenstein series 64 64 0

## Trace form

 $$928 q - 8 q^{3} - 12 q^{6} + 140 q^{7} + O(q^{10})$$ $$928 q - 8 q^{3} - 12 q^{6} + 140 q^{7} - 2160 q^{10} - 1628 q^{12} + 1036 q^{13} + 1906 q^{15} + 53224 q^{16} + 122 q^{18} - 1992 q^{21} - 3400 q^{22} + 1032 q^{25} + 2866 q^{27} - 18892 q^{28} - 12506 q^{30} + 9656 q^{31} + 36278 q^{33} + 40196 q^{36} - 46264 q^{37} + 39812 q^{40} + 73094 q^{42} + 81920 q^{43} + 8612 q^{45} - 62904 q^{46} - 18746 q^{48} + 9868 q^{51} + 209772 q^{52} + 52888 q^{55} - 173730 q^{57} + 147052 q^{58} + 208390 q^{60} - 68304 q^{61} - 152414 q^{63} - 263420 q^{66} + 8448 q^{67} + 219340 q^{70} - 143068 q^{72} + 179360 q^{73} - 150766 q^{75} + 127312 q^{76} + 166820 q^{78} + 22708 q^{81} + 380572 q^{82} - 263532 q^{85} + 91164 q^{87} - 1922416 q^{88} + 1852576 q^{90} + 118336 q^{91} + 61372 q^{93} - 389656 q^{96} - 389256 q^{97} + O(q^{100})$$

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

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