Properties

Label 4000.1.b
Level $4000$
Weight $1$
Character orbit 4000.b
Rep. character $\chi_{4000}(2751,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $600$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4000 = 2^{5} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 4000.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(600\)
Trace bound: \(13\)

Dimensions

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

Total New Old
Modular forms 76 8 68
Cusp forms 36 8 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 0 0 0 8

Trace form

\( 8q - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{9} - 4q^{21} - 8q^{29} + 8q^{41} - 4q^{61} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4000.1.b.a \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) \(A_{5}\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{3}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
4000.1.b.b \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) \(A_{5}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-\beta _{3}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)