Properties

Label 2001.1.bf
Level $2001$
Weight $1$
Character orbit 2001.bf
Rep. character $\chi_{2001}(68,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $72$
Newform subspaces $4$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2001 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2001, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 72 72 0
Eisenstein series 48 48 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 72 0 0 0

Trace form

\( 72 q + O(q^{10}) \) \( 72 q - 6 q^{12} + 12 q^{16} + 6 q^{18} - 12 q^{24} - 12 q^{25} - 6 q^{27} + 12 q^{36} + 6 q^{39} - 12 q^{49} + 12 q^{58} - 84 q^{64} + 36 q^{72} - 6 q^{87} - 24 q^{94} - 42 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2001, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2001.1.bf.a 2001.bf 2001.af $12$ $0.999$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots\)
2001.1.bf.b 2001.bf 2001.af $12$ $0.999$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-23}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2001.1.bf.c 2001.bf 2001.af $24$ $0.999$ \(\Q(\zeta_{84})\) $D_{84}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots\)
2001.1.bf.d 2001.bf 2001.af $24$ $0.999$ \(\Q(\zeta_{84})\) $D_{84}$ \(\Q(\sqrt{-23}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots\)