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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.2.m.a 228.m 228.m $72$ $1.821$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$