Properties

Label 2009.1.i
Level 2009
Weight 1
Character orbit i
Rep. character \(\chi_{2009}(901,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 12
Newform subspaces 2
Sturm bound 196
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2009.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(196\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2009, [\chi])\).

Total New Old
Modular forms 28 20 8
Cusp forms 12 12 0
Eisenstein series 16 8 8

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

\( 12q + 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} - 2q^{16} + 6q^{18} + 2q^{23} - 6q^{25} + 6q^{32} - 4q^{36} + 2q^{37} + 4q^{39} - 4q^{43} + 4q^{46} - 4q^{50} + 4q^{51} - 8q^{57} - 2q^{72} - 10q^{74} + 12q^{78} - 2q^{81} + 4q^{86} + 16q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2009, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2009.1.i.a \(6\) \(1.003\) 6.0.64827.1 \(D_{7}\) \(\Q(\sqrt{-287}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
2009.1.i.b \(6\) \(1.003\) 6.0.64827.1 \(D_{7}\) \(\Q(\sqrt{-287}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$3$ (\( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$5$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$7$ 1
$11$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$13$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))
$17$ (\( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$19$ (\( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$23$ (\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$29$ (\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$31$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$37$ (\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$41$ (\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))
$43$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))
$47$ (\( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$53$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$59$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$61$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$67$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$71$ (\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$73$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$79$ (\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{3}( 1 + T + T^{2} )^{3} \))
$83$ (\( ( 1 - T )^{6}( 1 + T )^{6} \))(\( ( 1 - T )^{6}( 1 + T )^{6} \))
$89$ (\( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} \))(\( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} \))
$97$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))
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