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Properties

Label 1503.1.f
Level $1503$
Weight $1$
Character orbit 1503.f
Rep. character $\chi_{1503}(166,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1503.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1503 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1503, [\chi])\).

Total New Old
Modular forms 26 26 0
Cusp forms 22 22 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 22 0 0 0

Trace form

\( 22 q - 11 q^{4} + O(q^{10}) \) \( 22 q - 11 q^{4} - 11 q^{16} - 11 q^{25} - 11 q^{42} - 22 q^{44} + 22 q^{48} - 11 q^{49} - 11 q^{54} + 44 q^{62} + 22 q^{64} - 11 q^{72} + 22 q^{84} - 22 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1503, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1503.1.f.a 1503.f 1503.f $2$ $0.750$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-167}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{6}+\zeta_{6}q^{7}+\cdots\)
1503.1.f.b 1503.f 1503.f $20$ $0.750$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-167}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q+(-\zeta_{66}^{9}-\zeta_{66}^{13})q^{2}+\zeta_{66}^{14}q^{3}+\cdots\)