Properties

Label 2004.1.g
Level $2004$
Weight $1$
Character orbit 2004.g
Rep. character $\chi_{2004}(2003,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $6$
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: \(\Q\)
Newform subspaces: \( 6 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2004, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2004.1.g.a 2004.g 2004.g $1$ $1.000$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2004.1.g.b 2004.g 2004.g $1$ $1.000$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2004.1.g.c 2004.g 2004.g $2$ $1.000$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-501}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2004.1.g.d 2004.g 2004.g $2$ $1.000$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-501}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2004.1.g.e 2004.g 2004.g $10$ $1.000$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-167}) \) 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 2004.g 2004.g $10$ $1.000$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-167}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots\)