Properties

Label 81.3.h
Level $81$
Weight $3$
Character orbit 81.h
Rep. character $\chi_{81}(2,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $306$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 81.h (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(81, [\chi])\).

Total New Old
Modular forms 342 342 0
Cusp forms 306 306 0
Eisenstein series 36 36 0

Trace form

\( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 90 q^{18} - 18 q^{19} - 234 q^{20} - 153 q^{21} - 18 q^{22} - 99 q^{23} - 126 q^{24} - 18 q^{25} - 27 q^{26} + 9 q^{27} - 9 q^{28} + 63 q^{29} + 198 q^{30} - 18 q^{31} + 306 q^{32} + 171 q^{33} - 18 q^{34} + 225 q^{35} + 342 q^{36} - 18 q^{37} + 90 q^{38} - 18 q^{39} - 18 q^{40} - 234 q^{41} - 513 q^{42} - 18 q^{43} - 666 q^{44} - 450 q^{45} - 18 q^{46} - 342 q^{47} - 513 q^{48} - 18 q^{49} - 369 q^{50} - 144 q^{51} - 54 q^{52} - 27 q^{53} + 108 q^{54} - 9 q^{55} + 396 q^{56} + 198 q^{57} - 18 q^{58} + 360 q^{59} + 801 q^{60} - 18 q^{61} + 873 q^{62} + 522 q^{63} - 18 q^{64} + 1170 q^{65} + 1926 q^{66} - 369 q^{67} + 2169 q^{68} + 1062 q^{69} - 558 q^{70} + 630 q^{71} + 1710 q^{72} - 18 q^{73} + 846 q^{74} + 432 q^{75} - 342 q^{76} + 414 q^{77} + 189 q^{78} - 72 q^{79} - 90 q^{81} - 36 q^{82} - 234 q^{83} - 945 q^{84} + 252 q^{85} - 882 q^{86} - 1026 q^{87} + 630 q^{88} - 1314 q^{89} - 2529 q^{90} - 18 q^{91} - 3960 q^{92} - 2214 q^{93} + 738 q^{94} - 2394 q^{95} - 3321 q^{96} + 441 q^{97} - 2853 q^{98} - 1566 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.3.h.a 81.h 81.h $306$ $2.207$ None \(-18\) \(-18\) \(-18\) \(-18\) $\mathrm{SU}(2)[C_{54}]$