# Properties

 Label 165.6.s Level $165$ Weight $6$ Character orbit 165.s Rep. character $\chi_{165}(4,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $240$ Sturm bound $144$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.s (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$144$$

## Dimensions

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

Total New Old
Modular forms 496 240 256
Cusp forms 464 240 224
Eisenstein series 32 0 32

## Trace form

 $$240 q + 960 q^{4} - 44 q^{5} + 144 q^{6} + 4860 q^{9} + O(q^{10})$$ $$240 q + 960 q^{4} - 44 q^{5} + 144 q^{6} + 4860 q^{9} - 72 q^{10} - 336 q^{11} + 3880 q^{14} - 990 q^{15} - 6944 q^{16} - 5424 q^{19} + 13046 q^{20} - 14112 q^{21} - 6912 q^{24} - 286 q^{25} + 46660 q^{26} + 10404 q^{30} - 24772 q^{31} + 15680 q^{34} + 7480 q^{35} - 77760 q^{36} - 35496 q^{39} + 46058 q^{40} + 24924 q^{41} - 232524 q^{44} + 3564 q^{45} + 20392 q^{46} + 266908 q^{49} + 131582 q^{50} + 57276 q^{51} + 46656 q^{54} + 47100 q^{55} + 478320 q^{56} + 60636 q^{59} - 32292 q^{60} - 106552 q^{61} - 397196 q^{64} - 359300 q^{65} - 3132 q^{66} + 62172 q^{69} + 101696 q^{70} - 144736 q^{71} - 258808 q^{74} + 202680 q^{75} - 721328 q^{76} - 230788 q^{79} + 302502 q^{80} - 393660 q^{81} - 332424 q^{84} - 238330 q^{85} + 801968 q^{86} - 81400 q^{89} - 109188 q^{90} + 425480 q^{91} - 949724 q^{94} + 622838 q^{95} + 258048 q^{96} + 27216 q^{99} + O(q^{100})$$

## 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

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