Properties

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

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{9})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(27, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.2.e.a \(12\) \(0.216\) 12.0.\(\cdots\).1 None \(-6\) \(-6\) \(-3\) \(-6\) \(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)