Properties

Label 228.2.k
Level $228$
Weight $2$
Character orbit 228.k
Rep. character $\chi_{228}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $2$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(23\)

Dimensions

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

Total New Old
Modular forms 88 40 48
Cusp forms 72 40 32
Eisenstein series 16 0 16

Trace form

\( 40q + 2q^{4} - 2q^{6} - 20q^{9} + O(q^{10}) \) \( 40q + 2q^{4} - 2q^{6} - 20q^{9} + 12q^{10} + 12q^{13} + 18q^{14} + 2q^{16} - 28q^{20} + 12q^{21} + 4q^{24} - 20q^{25} + 14q^{28} - 60q^{32} - 36q^{34} + 2q^{36} + 14q^{38} - 72q^{40} + 24q^{41} + 18q^{44} - 24q^{48} - 48q^{49} + 6q^{52} - 24q^{53} - 2q^{54} + 12q^{57} + 32q^{58} + 6q^{60} + 20q^{61} - 26q^{62} - 28q^{64} - 16q^{66} + 80q^{68} + 72q^{70} + 18q^{72} - 12q^{73} + 48q^{74} - 66q^{76} - 64q^{77} + 66q^{78} + 62q^{80} - 20q^{81} - 36q^{82} + 16q^{85} - 18q^{86} - 48q^{89} - 12q^{90} + 18q^{92} + 12q^{93} + 4q^{96} - 24q^{97} - 12q^{98} + O(q^{100}) \)

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.k.a \(20\) \(1.821\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-1\) \(-10\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{12}q^{3}+\beta _{9}q^{4}+(\beta _{6}-\beta _{17}+\cdots)q^{5}+\cdots\)
228.2.k.b \(20\) \(1.821\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1\) \(10\) \(0\) \(0\) \(q+(-\beta _{8}-\beta _{16})q^{2}-\beta _{11}q^{3}+\beta _{17}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)