Properties

Label 81.9.h
Level $81$
Weight $9$
Character orbit 81.h
Rep. character $\chi_{81}(2,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1278$
Newform subspaces $1$
Sturm bound $81$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(81\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(81, [\chi])\).

Total New Old
Modular forms 1314 1314 0
Cusp forms 1278 1278 0
Eisenstein series 36 36 0

Trace form

\( 1278 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1278 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 274194 q^{18} - 18 q^{19} - 677394 q^{20} - 1360953 q^{21} - 18 q^{22} + 932049 q^{23} + 3725550 q^{24} - 18 q^{25} - 27 q^{26} - 1933299 q^{27} - 9 q^{28} - 2853729 q^{29} - 1292562 q^{30} - 18 q^{31} + 11466990 q^{32} + 6069339 q^{33} - 18 q^{34} - 6225435 q^{35} - 18224658 q^{36} - 18 q^{37} + 12749166 q^{38} - 18 q^{39} - 18 q^{40} - 6454962 q^{41} + 39542067 q^{42} - 18 q^{43} - 17341146 q^{44} - 37896786 q^{45} - 18 q^{46} - 19806786 q^{47} + 15217767 q^{48} - 18 q^{49} + 104798403 q^{50} + 54355878 q^{51} - 2322 q^{52} - 27 q^{53} - 75728412 q^{54} - 9 q^{55} - 168854472 q^{56} - 65747826 q^{57} - 18 q^{58} + 7377030 q^{59} + 125543673 q^{60} - 18 q^{61} + 223709589 q^{62} + 101958462 q^{63} - 18 q^{64} - 45382806 q^{65} - 552090186 q^{66} + 95245587 q^{67} - 190809207 q^{68} + 273910662 q^{69} - 177120018 q^{70} + 251437590 q^{71} + 548536302 q^{72} - 18 q^{73} - 154054674 q^{74} - 246093768 q^{75} + 305980398 q^{76} - 574220898 q^{77} - 478793403 q^{78} + 103151808 q^{79} + 148365990 q^{81} - 36 q^{82} + 368657334 q^{83} + 1377777303 q^{84} - 257411268 q^{85} + 435234798 q^{86} + 61361982 q^{87} + 213663726 q^{88} - 893853972 q^{89} - 624764277 q^{90} - 18 q^{91} - 745285608 q^{92} - 53952426 q^{93} - 106493202 q^{94} - 313936362 q^{95} + 626058639 q^{96} - 427023783 q^{97} - 590433561 q^{98} - 967332078 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.9.h.a 81.h 81.h $1278$ $32.998$ None \(-18\) \(-18\) \(-18\) \(-18\) $\mathrm{SU}(2)[C_{54}]$