Properties

Label 1003.1.b
Level $1003$
Weight $1$
Character orbit 1003.b
Rep. character $\chi_{1003}(1002,\cdot)$
Character field $\Q$
Dimension $3$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q\)
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 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q + 3 q^{4} - 3 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{4} - 3 q^{9} + 6 q^{15} + 3 q^{16} - 3 q^{17} + 6 q^{21} - 3 q^{25} - 6 q^{35} - 3 q^{36} - 3 q^{49} - 3 q^{59} + 6 q^{60} + 3 q^{64} - 3 q^{68} + 3 q^{81} + 6 q^{84} - 6 q^{87} + O(q^{100}) \)

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.b.a 1003.b 1003.b $1$ $0.501$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b 1003.b 1003.b $2$ $0.501$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)