Properties

Label 228.2.f
Level $228$
Weight $2$
Character orbit 228.f
Rep. character $\chi_{228}(151,\cdot)$
Character field $\Q$
Dimension $20$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(31\)

Dimensions

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

Total New Old
Modular forms 44 20 24
Cusp forms 36 20 16
Eisenstein series 8 0 8

Trace form

\( 20q + 4q^{4} - 4q^{6} + 20q^{9} + O(q^{10}) \) \( 20q + 4q^{4} - 4q^{6} + 20q^{9} + 4q^{16} - 32q^{20} - 4q^{24} + 20q^{25} - 32q^{28} + 4q^{36} - 8q^{38} - 48q^{44} - 12q^{49} - 4q^{54} - 12q^{57} + 40q^{58} - 56q^{61} - 16q^{62} + 4q^{64} + 40q^{66} - 32q^{68} - 24q^{73} + 36q^{76} - 8q^{77} + 88q^{80} + 20q^{81} + 24q^{82} - 40q^{85} + 72q^{92} - 24q^{93} - 4q^{96} + O(q^{100}) \)

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.f.a \(10\) \(1.821\) 10.0.\(\cdots\).1 None \(-2\) \(10\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
228.2.f.b \(10\) \(1.821\) 10.0.\(\cdots\).1 None \(2\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)

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

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