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Properties

Label 162.7.h
Level $162$
Weight $7$
Character orbit 162.h
Rep. character $\chi_{162}(5,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $972$
Sturm bound $189$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.h (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(189\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(162, [\chi])\).

Total New Old
Modular forms 2952 972 1980
Cusp forms 2880 972 1908
Eisenstein series 72 0 72

Trace form

\( 972 q + O(q^{10}) \) \( 972 q + 33120 q^{18} - 41472 q^{20} - 41040 q^{21} + 136080 q^{23} - 112320 q^{27} - 252720 q^{29} - 223776 q^{30} + 302400 q^{33} + 536544 q^{35} + 92160 q^{36} - 343440 q^{38} + 467208 q^{41} - 582768 q^{45} + 374220 q^{47} + 882378 q^{51} - 1372680 q^{57} - 1225854 q^{59} + 1778220 q^{63} - 2573208 q^{65} + 262080 q^{66} - 2291328 q^{67} + 984960 q^{68} + 4444704 q^{69} - 1782000 q^{70} + 1710720 q^{71} - 700416 q^{72} - 6106752 q^{74} - 9000000 q^{75} + 1373760 q^{76} - 13042944 q^{77} - 4901760 q^{78} + 1988064 q^{79} + 2787840 q^{81} + 7672320 q^{83} + 2310912 q^{84} - 7452000 q^{85} + 9590400 q^{86} + 16240896 q^{87} - 1036800 q^{88} + 4580550 q^{89} - 2448000 q^{90} - 5930496 q^{92} - 17804268 q^{93} + 6631632 q^{94} - 21325032 q^{95} - 1474560 q^{96} + 352512 q^{97} + 8786880 q^{98} + 26461584 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)