Properties

Label 588.1.p
Level $588$
Weight $1$
Character orbit 588.p
Rep. character $\chi_{588}(557,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 588.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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 54 2 52
Cusp forms 6 2 4
Eisenstein series 48 0 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + q^{3} - q^{9} + O(q^{10}) \) \( 2 q + q^{3} - q^{9} + 2 q^{13} - q^{19} - q^{25} - 2 q^{27} - q^{31} + q^{37} + q^{39} - 2 q^{43} - 2 q^{57} + 2 q^{61} + q^{67} - q^{73} + q^{75} + q^{79} - q^{81} + q^{93} - 4 q^{97} + O(q^{100}) \)

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.p.a $2$ $0.293$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)