Properties

Label 228.2.m
Level $228$
Weight $2$
Character orbit 228.m
Rep. character $\chi_{228}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{6})\)
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 88 88 0
Cusp forms 72 72 0
Eisenstein series 16 16 0

Trace form

\( 72q + 3q^{6} + O(q^{10}) \) \( 72q + 3q^{6} - 8q^{10} - 10q^{12} - 4q^{16} - 22q^{18} + 4q^{21} - 6q^{22} + 11q^{24} + 16q^{25} + 6q^{28} - 60q^{30} - 30q^{33} - 20q^{34} - 11q^{36} - 8q^{37} + 36q^{40} + 8q^{42} - 28q^{45} - 8q^{46} - 23q^{48} - 16q^{49} + 6q^{52} - 22q^{54} - 6q^{57} - 80q^{58} - 14q^{60} - 40q^{61} + 48q^{64} - 15q^{66} + 4q^{69} + 72q^{70} + 15q^{72} - 4q^{73} + 12q^{76} + 44q^{78} + 4q^{81} - 6q^{82} + 56q^{84} - 52q^{85} - 44q^{88} + 20q^{90} + 4q^{93} + 56q^{94} - 86q^{96} - 16q^{97} + O(q^{100}) \)

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.m.a \(72\) \(1.821\) None \(0\) \(0\) \(0\) \(0\)