Properties

Label 27.2.e
Level $27$
Weight $2$
Character orbit 27.e
Rep. character $\chi_{27}(4,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $12$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(27, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 12 12 0
Eisenstein series 12 12 0

Trace form

\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.2.e.a 27.e 27.e $12$ $0.216$ 12.0.\(\cdots\).1 None 27.2.e.a \(-6\) \(-6\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)