Properties

Label 2001.1.i
Level 2001
Weight 1
Character orbit 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

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

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2001.1.i.a \(2\) \(0.999\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-23}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots\)
2001.1.i.b \(2\) \(0.999\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-23}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots\)
2001.1.i.c \(4\) \(0.999\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-23}) \) 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 \(4\) \(0.999\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-23}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$3$ (\( ( 1 - T )^{2} \))(\( 1 + T^{2} \))(\( 1 - T^{2} + T^{4} \))(\( ( 1 + T + T^{2} )^{2} \))
$5$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))
$7$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))
$11$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$13$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))
$17$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$19$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$23$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$29$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} \))
$31$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$37$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$41$ (\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$43$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$47$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$53$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$59$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$61$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$67$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$71$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))
$73$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))
$79$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$83$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))
$89$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$97$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
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