Properties

Label 2000.1.z
Level 2000
Weight 1
Character orbit z
Rep. character \(\chi_{2000}(351,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 300
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2000 = 2^{4} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2000.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(300\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2000, [\chi])\).

Total New Old
Modular forms 164 8 156
Cusp forms 44 8 36
Eisenstein series 120 0 120

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q - 2q^{9} + O(q^{10}) \) \( 8q - 2q^{9} + 4q^{29} + 4q^{41} + 8q^{49} + 4q^{61} - 2q^{81} - 6q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2000, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2000.1.z.a \(8\) \(0.998\) \(\Q(\zeta_{20})\) \(D_{10}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{8}q^{9}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{13}+(\zeta_{20}^{3}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 3}\)