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Properties

Label 597.1.s
Level $597$
Weight $1$
Character orbit 597.s
Rep. character $\chi_{597}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $66$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 597 = 3 \cdot 199 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 597.s (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 597 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(66\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(597, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + q^{3} + q^{4} - q^{7} + q^{9} + O(q^{10}) \) \( 20 q + q^{3} + q^{4} - q^{7} + q^{9} - 2 q^{12} - q^{13} + q^{16} - q^{19} - q^{21} - 2 q^{25} - 2 q^{27} - 9 q^{28} - q^{31} + q^{36} + 2 q^{37} - q^{39} + 2 q^{43} + q^{48} - 9 q^{52} - q^{57} - 9 q^{61} + 2 q^{63} - 2 q^{64} + 2 q^{67} - q^{73} + q^{75} + 2 q^{76} + 2 q^{79} + q^{81} - q^{84} + q^{91} - 20 q^{93} - q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(597, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
597.1.s.a 597.s 597.s $20$ $0.298$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q-\zeta_{66}^{7}q^{3}+\zeta_{66}^{32}q^{4}+(\zeta_{66}^{12}-\zeta_{66}^{29}+\cdots)q^{7}+\cdots\)