Properties

Label 216.2.v
Level $216$
Weight $2$
Character orbit 216.v
Rep. character $\chi_{216}(11,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $204$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.v (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

Total New Old
Modular forms 228 228 0
Cusp forms 204 204 0
Eisenstein series 24 24 0

Trace form

\( 204 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} + O(q^{10}) \) \( 204 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 15 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 15 q^{18} - 6 q^{19} - 27 q^{20} - 6 q^{22} - 30 q^{24} - 12 q^{25} - 12 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 24 q^{33} - 12 q^{34} - 18 q^{35} - 36 q^{36} - 30 q^{38} + 9 q^{40} - 6 q^{42} - 12 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 30 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} + 6 q^{57} - 33 q^{58} - 48 q^{59} - 54 q^{60} + 90 q^{62} - 3 q^{64} - 12 q^{65} + 87 q^{66} - 12 q^{67} - 9 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 6 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 78 q^{86} - 30 q^{88} - 18 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} + 18 q^{96} - 12 q^{97} + 162 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.2.v.a $12$ $1.725$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}-2\beta _{4}q^{4}+\cdots\)
216.2.v.b $192$ $1.725$ None \(-6\) \(-12\) \(0\) \(0\)