Properties

Label 2003.1.b
Level $2003$
Weight $1$
Character orbit 2003.b
Rep. character $\chi_{2003}(2002,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $167$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2003 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2003.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2003 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(167\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2003, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - q^{3} + 4 q^{4} + 3 q^{9} + O(q^{10}) \) \( 4 q - q^{3} + 4 q^{4} + 3 q^{9} - q^{12} - q^{13} + 4 q^{16} - q^{19} + 4 q^{25} - 2 q^{27} + 3 q^{36} - 2 q^{39} - q^{47} - q^{48} + 4 q^{49} - q^{52} - q^{53} - 2 q^{57} - q^{59} + 4 q^{64} - q^{73} - q^{75} - q^{76} - q^{79} + 2 q^{81} - q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2003, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2003.1.b.a 2003.b 2003.b $1$ $1.000$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2003}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots\)
2003.1.b.b 2003.b 2003.b $3$ $1.000$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-2003}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots\)