# Properties

 Label 165.6.d Level $165$ Weight $6$ Character orbit 165.d Rep. character $\chi_{165}(164,\cdot)$ Character field $\Q$ Dimension $116$ Sturm bound $144$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ Character field: $$\Q$$ Sturm bound: $$144$$

## Dimensions

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

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

## Trace form

 $$116 q - 1800 q^{4} - 286 q^{9} + O(q^{10})$$ $$116 q - 1800 q^{4} - 286 q^{9} - 1023 q^{15} + 31976 q^{16} - 4366 q^{25} + 412 q^{31} - 1512 q^{34} - 11444 q^{36} - 51173 q^{45} + 237252 q^{49} - 15074 q^{55} - 84504 q^{60} - 439896 q^{64} + 47580 q^{66} + 99534 q^{69} - 73584 q^{70} + 250233 q^{75} - 163846 q^{81} - 230400 q^{91} + 177622 q^{99} + O(q^{100})$$

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

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