Properties

Label 4000.1.p
Level 4000
Weight 1
Character orbit p
Rep. character \(\chi_{4000}(193,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 16
Newforms 2
Sturm bound 600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 4000.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(600\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 114 16 98
Cusp forms 34 16 18
Eisenstein series 80 0 80

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\(16q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.p.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(D_{20}\) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-\zeta_{20}+\zeta_{20}^{4})q^{3}+(\zeta_{20}^{7}-\zeta_{20}^{8}+\cdots)q^{7}+\cdots\)
4000.1.p.b \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(D_{20}\) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)