Properties

Label 4000.1.bh
Level 4000
Weight 1
Character orbit bh
Rep. character \(\chi_{4000}(351,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
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.bh (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 100 \)
Character field: \(\Q(\zeta_{10})\)
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 248 8 240
Cusp forms 88 8 80
Eisenstein series 160 0 160

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

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

Trace form

\(8q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.bh.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(A_{5}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{3}+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)