Properties

Label 608.1.bg
Level $608$
Weight $1$
Character orbit 608.bg
Rep. character $\chi_{608}(47,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 608.bg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(608, [\chi])\).

Total New Old
Modular forms 72 18 54
Cusp forms 24 6 18
Eisenstein series 48 12 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

\( 6 q + 3 q^{3} - 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{3} - 3 q^{9} - 3 q^{27} - 3 q^{33} - 3 q^{41} - 3 q^{49} - 3 q^{51} + 3 q^{59} + 3 q^{67} + 6 q^{73} + 3 q^{81} - 3 q^{97} - 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.1.bg.a 608.bg 152.u $6$ $0.303$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(0\) \(3\) \(0\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{6})q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)