# Properties

 Label 162.9.h Level $162$ Weight $9$ Character orbit 162.h Rep. character $\chi_{162}(5,\cdot)$ Character field $\Q(\zeta_{54})$ Dimension $1296$ Sturm bound $243$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 162.h (of order $$54$$ and degree $$18$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$81$$ Character field: $$\Q(\zeta_{54})$$ Sturm bound: $$243$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(162, [\chi])$$.

Total New Old
Modular forms 3924 1296 2628
Cusp forms 3852 1296 2556
Eisenstein series 72 0 72

## Trace form

 $$1296 q + O(q^{10})$$ $$1296 q + 274176 q^{18} + 338688 q^{20} + 2721870 q^{21} - 1864134 q^{23} + 3866562 q^{27} + 5707422 q^{29} + 1292544 q^{30} - 12138714 q^{33} + 12450834 q^{35} + 9112320 q^{36} - 12749184 q^{38} + 6454944 q^{41} + 37896768 q^{45} + 19806768 q^{47} - 54355896 q^{51} + 65747808 q^{57} - 7377048 q^{59} - 101958480 q^{63} + 15885288 q^{65} + 297787392 q^{66} - 190491210 q^{67} + 15869952 q^{68} - 398223792 q^{69} + 177120000 q^{70} - 502875216 q^{71} - 182845440 q^{72} + 154054656 q^{74} + 492187500 q^{75} - 101993472 q^{76} + 1148441760 q^{77} + 478734336 q^{78} - 206303652 q^{79} - 296732016 q^{81} - 737314704 q^{83} - 196816896 q^{84} + 514822500 q^{85} - 435234816 q^{86} - 122724000 q^{87} - 71221248 q^{88} + 1140352668 q^{89} + 1128960000 q^{90} + 529735680 q^{92} + 497955456 q^{93} + 106493184 q^{94} - 797009328 q^{95} - 264241152 q^{96} + 854047530 q^{97} - 468467712 q^{98} + 1648813176 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(162, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{9}^{\mathrm{old}}(162, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(162, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$