Properties

Label 4000.1.e
Level 4000
Weight 1
Character orbit e
Rep. character \(\chi_{4000}(1999,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 600
Trace bound 7

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Defining parameters

Level: \( N \) = \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 4000.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(600\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 72 4 68
Cusp forms 32 4 28
Eisenstein series 40 0 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut +\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.e.a \(2\) \(1.996\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
4000.1.e.b \(2\) \(1.996\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 3}\)