Properties

Label 133.1.m
Level 133
Weight 1
Character orbit m
Rep. character \(\chi_{133}(83,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 13
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 133.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(133, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q - 2q^{2} - 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{8} - 2q^{15} + 2q^{16} + 2q^{21} - 2q^{23} + 2q^{29} + 4q^{30} - 2q^{35} - 4q^{39} + 2q^{42} - 2q^{43} + 4q^{46} - 4q^{49} + 2q^{51} + 2q^{53} - 2q^{57} - 4q^{58} + 4q^{64} + 4q^{65} - 2q^{67} - 2q^{70} + 2q^{71} + 2q^{78} - 2q^{79} + 2q^{81} - 2q^{85} - 2q^{86} + 2q^{91} + 2q^{95} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(133, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
133.1.m.a \(4\) \(0.066\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots\)

Hecke characteristic polynomials

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