Properties

Label 27.5.f
Level $27$
Weight $5$
Character orbit 27.f
Rep. character $\chi_{27}(2,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $66$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(27, [\chi])\).

Total New Old
Modular forms 78 78 0
Cusp forms 66 66 0
Eisenstein series 12 12 0

Trace form

\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} + O(q^{10}) \) \( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19} - 2487 q^{20} - 2784 q^{21} + 1002 q^{22} - 2724 q^{23} - 3312 q^{24} + 435 q^{25} + 1368 q^{27} - 12 q^{28} + 5016 q^{29} + 10773 q^{30} - 1671 q^{31} + 10224 q^{32} + 2925 q^{33} - 342 q^{34} - 2682 q^{35} - 7704 q^{36} - 3 q^{37} - 6564 q^{38} - 1983 q^{39} - 1113 q^{40} + 5754 q^{41} + 8694 q^{42} - 1266 q^{43} - 4545 q^{44} - 7029 q^{45} - 3 q^{46} - 9159 q^{47} - 28383 q^{48} + 5898 q^{49} - 34977 q^{50} - 14814 q^{51} + 2871 q^{52} + 13878 q^{54} - 12 q^{55} + 39243 q^{56} + 15792 q^{57} - 12291 q^{58} + 24762 q^{59} + 50670 q^{60} - 8358 q^{61} + 38304 q^{62} + 21609 q^{63} + 6141 q^{64} + 23727 q^{65} + 11349 q^{66} + 15996 q^{67} - 43533 q^{68} - 26847 q^{69} - 7251 q^{70} - 19773 q^{71} - 77580 q^{72} + 6108 q^{73} - 74847 q^{74} - 49155 q^{75} - 28614 q^{76} - 33909 q^{77} - 9108 q^{78} - 5658 q^{79} - 12600 q^{81} - 12 q^{82} + 18813 q^{83} + 82356 q^{84} + 24219 q^{85} + 96474 q^{86} + 84555 q^{87} + 36042 q^{88} + 110232 q^{89} + 153540 q^{90} - 6042 q^{91} + 73545 q^{92} + 1293 q^{93} + 2631 q^{94} - 65163 q^{95} - 152226 q^{96} - 3696 q^{97} - 259938 q^{98} - 162405 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.5.f.a 27.f 27.f $66$ $2.791$ None \(-6\) \(-6\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{18}]$