Properties

Label 162.3.h
Level $162$
Weight $3$
Character orbit 162.h
Rep. character $\chi_{162}(5,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $324$
Newform subspaces $1$
Sturm bound $81$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.h (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(162, [\chi])\).

Total New Old
Modular forms 1008 324 684
Cusp forms 936 324 612
Eisenstein series 72 0 72

Trace form

\( 324 q + O(q^{10}) \) \( 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.3.h.a 162.h 81.h $324$ $4.414$ None 162.3.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{54}]$

Decomposition of \(S_{3}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)