Properties

Label 2003.1.b
Level 2003
Weight 1
Character orbit b
Rep. character \(\chi_{2003}(2002,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2003, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2003.1.b.a \(1\) \(1.000\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2003}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots\)
2003.1.b.b \(3\) \(1.000\) \(\Q(\zeta_{18})^+\) \(D_{9}\) \(\Q(\sqrt{-2003}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots\)