Properties

Label 228.1.s
Level $228$
Weight $1$
Character orbit 228.s
Rep. character $\chi_{228}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 228.s (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(228, [\chi])\).

Total New Old
Modular forms 42 6 36
Cusp forms 6 6 0
Eisenstein series 36 0 36

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q - 3 q^{13} - 3 q^{19} - 3 q^{21} - 3 q^{27} - 3 q^{43} - 3 q^{49} + 6 q^{61} + 6 q^{63} - 3 q^{67} - 3 q^{73} + 6 q^{75} + 6 q^{79} + 6 q^{91} + 6 q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.1.s.a 228.s 57.l $6$ $0.114$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots\)