Properties

Label 228.2.v
Level $228$
Weight $2$
Character orbit 228.v
Rep. character $\chi_{228}(23,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $216$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.v (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

Total New Old
Modular forms 264 264 0
Cusp forms 216 216 0
Eisenstein series 48 48 0

Trace form

\( 216q - 18q^{4} - 6q^{6} - 18q^{9} + O(q^{10}) \) \( 216q - 18q^{4} - 6q^{6} - 18q^{9} - 18q^{10} - 3q^{12} - 36q^{13} - 6q^{16} - 12q^{18} - 30q^{21} - 18q^{24} - 24q^{25} - 36q^{28} + 12q^{33} + 30q^{34} - 66q^{36} - 48q^{37} - 42q^{40} - 117q^{42} - 6q^{45} - 6q^{46} - 81q^{48} + 24q^{49} + 12q^{52} + 33q^{54} - 12q^{57} + 48q^{58} - 18q^{60} - 48q^{61} + 36q^{64} - 18q^{66} - 6q^{69} - 18q^{70} + 12q^{72} - 132q^{73} + 60q^{76} - 39q^{78} + 18q^{81} + 132q^{82} - 45q^{84} - 144q^{85} + 114q^{88} + 72q^{90} - 30q^{93} + 138q^{96} - 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
228.2.v.a \(216\) \(1.821\) None \(0\) \(0\) \(0\) \(0\)