Properties

Label 57.1.h
Level $57$
Weight $1$
Character orbit 57.h
Rep. character $\chi_{57}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(57, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.1.h.a 57.h 57.h $2$ $0.028$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)