Properties

Label 162.11.h
Level $162$
Weight $11$
Character orbit 162.h
Rep. character $\chi_{162}(5,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1620$
Sturm bound $297$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 162.h (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(297\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(162, [\chi])\).

Total New Old
Modular forms 4896 1620 3276
Cusp forms 4824 1620 3204
Eisenstein series 72 0 72

Trace form

\( 1620 q + O(q^{10}) \) \( 1620 q - 3053952 q^{18} + 15234048 q^{20} - 28173150 q^{21} - 3013362 q^{23} - 123046506 q^{27} - 67126158 q^{29} + 144526464 q^{30} - 122955462 q^{33} - 520307226 q^{35} + 135705600 q^{36} - 371017152 q^{38} - 385170120 q^{41} + 194789232 q^{45} - 1975444524 q^{47} + 3031812630 q^{51} - 1983447864 q^{57} + 4872115710 q^{59} - 4406834700 q^{63} + 6315602832 q^{65} + 17916772608 q^{66} + 3618579042 q^{67} - 4427495424 q^{68} - 34587102960 q^{69} + 1647000000 q^{70} + 22051648656 q^{71} + 18258591744 q^{72} + 16186452480 q^{74} - 10898437500 q^{75} + 5936274432 q^{76} - 89192440224 q^{77} - 42945311232 q^{78} + 19982165940 q^{79} + 29482836336 q^{81} + 62903796048 q^{83} + 13610373120 q^{84} - 20808562500 q^{85} - 11738663424 q^{86} - 107586841824 q^{87} + 16005758976 q^{88} - 115435280682 q^{89} - 70488000000 q^{90} + 29006290944 q^{92} + 144353719260 q^{93} - 57745154880 q^{94} + 126091272888 q^{95} - 3321888768 q^{96} + 77817729942 q^{97} - 144353062656 q^{98} - 18892680552 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

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

Decomposition of \(S_{11}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)