Properties

Label 588.1.z
Level $588$
Weight $1$
Character orbit 588.z
Rep. character $\chi_{588}(53,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 588.z (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(588, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + q^{3} + q^{7} + q^{9} + O(q^{10}) \) \( 12 q + q^{3} + q^{7} + q^{9} + 2 q^{13} - q^{19} - 2 q^{21} + q^{25} - 2 q^{27} - q^{31} - 8 q^{37} - 8 q^{39} + 2 q^{43} + q^{49} + 2 q^{57} - 5 q^{61} - 6 q^{63} - q^{67} - q^{73} + q^{75} - q^{79} + q^{81} - q^{91} - q^{93} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.1.z.a $12$ $0.293$ \(\Q(\zeta_{21})\) $D_{21}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots\)