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Properties

Label 162.8.g
Level $162$
Weight $8$
Character orbit 162.g
Rep. character $\chi_{162}(7,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1134$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(162, [\chi])\).

Total New Old
Modular forms 3438 1134 2304
Cusp forms 3366 1134 2232
Eisenstein series 72 0 72

Trace form

\( 1134 q + O(q^{10}) \) \( 1134 q - 108792 q^{18} + 81792 q^{20} - 372006 q^{21} - 421902 q^{23} + 949104 q^{26} + 833922 q^{27} - 540486 q^{29} - 1355184 q^{30} - 308502 q^{33} + 3469986 q^{35} + 1243008 q^{36} - 2149992 q^{38} - 2134206 q^{41} - 1459026 q^{45} - 6232518 q^{47} + 4677309 q^{51} + 8039358 q^{53} - 3123738 q^{57} - 13283739 q^{59} + 1006938 q^{63} + 46778814 q^{65} - 22506048 q^{66} + 26462322 q^{67} - 6903936 q^{68} - 42561702 q^{69} - 5238000 q^{70} + 42379344 q^{71} + 29159424 q^{72} + 49640832 q^{74} + 36562500 q^{75} - 603072 q^{76} - 48045024 q^{77} - 48198528 q^{78} + 49246596 q^{79} - 18432000 q^{80} - 70916976 q^{81} - 33504048 q^{83} - 675072 q^{84} - 23719500 q^{85} + 64923264 q^{86} + 184319136 q^{87} - 20307456 q^{88} + 118235709 q^{89} + 90864000 q^{90} - 1322496 q^{92} - 52912422 q^{93} + 52133328 q^{94} - 195638886 q^{95} - 25362432 q^{96} + 52249482 q^{97} + 21813696 q^{98} + 145779930 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)