Properties

Label 2011.1.b
Level 2011
Weight 1
Character orbit b
Rep. character \(\chi_{2011}(2010,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 1
Sturm bound 167
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2011 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2011.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2011 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(167\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2011, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3q + 3q^{4} - q^{5} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{4} - q^{5} + 3q^{9} - q^{13} + 3q^{16} - q^{20} - q^{23} + 2q^{25} - q^{31} + 3q^{36} - q^{41} - q^{43} - q^{45} + 3q^{49} - q^{52} + 3q^{64} - 2q^{65} - q^{71} - q^{80} + 3q^{81} - q^{83} - q^{89} - q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2011, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2011.1.b.a \(3\) \(1.004\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-2011}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$3$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$5$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$7$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$11$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$13$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$17$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$19$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$23$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$29$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$31$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$37$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$41$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$43$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$47$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$53$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$59$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$61$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$67$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$71$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$73$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$79$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$83$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$89$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$97$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
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