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Properties

Label 162.8.e
Level $162$
Weight $8$
Character orbit 162.e
Rep. character $\chi_{162}(19,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $126$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(216\)

Dimensions

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

Total New Old
Modular forms 1170 126 1044
Cusp forms 1098 126 972
Eisenstein series 72 0 72

Trace form

\( 126 q - 426 q^{5} - 1536 q^{8} + O(q^{10}) \) \( 126 q - 426 q^{5} - 1536 q^{8} + 18267 q^{11} - 26832 q^{14} - 58956 q^{17} + 54528 q^{20} - 105768 q^{22} - 284712 q^{23} + 215982 q^{25} + 632736 q^{26} - 264306 q^{29} - 595962 q^{31} + 266184 q^{34} + 642162 q^{35} - 399264 q^{38} - 1053903 q^{41} + 1080963 q^{43} - 511104 q^{44} - 4733640 q^{47} - 976014 q^{49} + 1347552 q^{50} + 5903952 q^{53} - 1717248 q^{56} - 4371630 q^{59} - 3865446 q^{61} - 5719872 q^{62} - 16515072 q^{64} + 4923066 q^{65} - 14387841 q^{67} + 7527936 q^{68} + 3492000 q^{70} - 7063224 q^{71} - 7541874 q^{73} - 23032272 q^{74} + 402048 q^{76} + 2583966 q^{77} - 32831064 q^{79} + 6144000 q^{80} + 7892640 q^{83} + 15813000 q^{85} - 25345656 q^{86} + 13538304 q^{88} - 54045951 q^{89} - 6630138 q^{91} + 9441408 q^{92} - 34755552 q^{94} + 57195498 q^{95} - 42777531 q^{97} - 29047800 q^{98} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)