Properties

Label 1003.1.f
Level $1003$
Weight $1$
Character orbit 1003.f
Rep. character $\chi_{1003}(353,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1003.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1003, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 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 6 0 0 0

Trace form

\( 6 q - 6 q^{4} + O(q^{10}) \) \( 6 q - 6 q^{4} + 6 q^{16} + 12 q^{21} - 6 q^{27} + 6 q^{45} - 6 q^{57} + 6 q^{63} - 6 q^{64} - 6 q^{71} + 6 q^{75} - 6 q^{81} - 12 q^{84} - 6 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1003.1.f.a 1003.f 1003.f $2$ $0.501$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-59}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b 1003.f 1003.f $4$ $0.501$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-59}) \) None \(0\) \(2\) \(2\) \(2\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)