Properties

Label 2004.1.g
Level 2004
Weight 1
Character orbit g
Rep. character \(\chi_{2004}(2003,\cdot)\)
Character field \(\Q\)
Dimension 26
Newforms 6
Sturm bound 336
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2004.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2004 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2004, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 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 26 0 0 0

Trace form

\(26q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut -\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 11q^{72} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 11q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2004, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2004.1.g.a \(1\) \(1.000\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2004.1.g.b \(1\) \(1.000\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2004.1.g.c \(2\) \(1.000\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-501}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2004.1.g.d \(2\) \(1.000\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-501}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2004.1.g.e \(10\) \(1.000\) \(\Q(\zeta_{22})\) \(D_{22}\) \(\Q(\sqrt{-167}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots\)
2004.1.g.f \(10\) \(1.000\) \(\Q(\zeta_{22})\) \(D_{22}\) \(\Q(\sqrt{-167}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots\)