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Properties

Label 2001.1.i
Level $2001$
Weight $1$
Character orbit 2001.i
Rep. character $\chi_{2001}(1172,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2001 \)
Character field: \(\Q(i)\)
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 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

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

Display 100 coefficients 10 coefficients

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.i.a 2001.i 2001.i $2$ $0.999$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots\)
2001.1.i.b 2001.i 2001.i $2$ $0.999$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-23}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots\)
2001.1.i.c 2001.i 2001.i $4$ $0.999$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2001.1.i.d 2001.i 2001.i $4$ $0.999$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-23}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)