Properties

Label 216.3.r
Level $216$
Weight $3$
Character orbit 216.r
Rep. character $\chi_{216}(43,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $420$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.r (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

Total New Old
Modular forms 444 444 0
Cusp forms 420 420 0
Eisenstein series 24 24 0

Trace form

\( 420q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 3q^{8} - 12q^{9} + O(q^{10}) \) \( 420q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 3q^{8} - 12q^{9} - 3q^{10} - 12q^{11} + 39q^{12} - 51q^{14} - 6q^{16} - 6q^{17} + 15q^{18} - 6q^{19} - 69q^{20} - 6q^{22} - 84q^{24} - 12q^{25} + 150q^{26} - 12q^{27} - 12q^{28} + 141q^{30} + 84q^{32} + 12q^{33} + 6q^{34} - 6q^{35} - 36q^{36} - 84q^{38} - 81q^{40} + 60q^{41} - 546q^{42} - 12q^{43} + 213q^{44} - 3q^{46} + 207q^{48} - 12q^{49} - 315q^{50} + 42q^{51} - 33q^{52} + 78q^{54} - 405q^{56} + 42q^{57} - 141q^{58} + 420q^{59} - 882q^{60} + 294q^{62} - 3q^{64} - 12q^{65} + 393q^{66} - 12q^{67} - 525q^{68} - 141q^{70} + 228q^{72} - 6q^{73} - 207q^{74} - 348q^{75} + 42q^{76} - 216q^{78} + 798q^{80} - 12q^{81} - 12q^{82} - 732q^{83} + 654q^{84} + 282q^{86} + 186q^{88} - 6q^{89} - 420q^{90} - 6q^{91} - 1077q^{92} + 345q^{94} - 1242q^{96} - 12q^{97} - 516q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.3.r.a \(12\) \(5.886\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}+4\beta _{4}q^{4}+\cdots\)
216.3.r.b \(408\) \(5.886\) None \(-6\) \(-12\) \(0\) \(0\)