Properties

Label 4000.1.cq
Level 4000
Weight 1
Character orbit cq
Rep. character \(\chi_{4000}(33,\cdot)\)
Character field \(\Q(\zeta_{100})\)
Dimension 40
Newforms 1
Sturm bound 600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 4000.cq (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 125 \)
Character field: \(\Q(\zeta_{100})\)
Newforms: \( 1 \)
Sturm bound: \(600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).

Total New Old
Modular forms 360 40 320
Cusp forms 40 40 0
Eisenstein series 320 0 320

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\(40q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(40q \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4000.1.cq.a \(40\) \(1.996\) \(\Q(\zeta_{100})\) \(D_{100}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots\)