Properties

Label 59.1.b
Level 59
Weight 1
Character orbit b
Rep. character \(\chi_{59}(58,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(59, [\chi])\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 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 1 0 0 0

Trace form

\( q - q^{3} + q^{4} - q^{5} - q^{7} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{5} - q^{7} - q^{12} + q^{15} + q^{16} + 2q^{17} - q^{19} - q^{20} + q^{21} + q^{27} - q^{28} - q^{29} + q^{35} - q^{41} - q^{48} - 2q^{51} - q^{53} + q^{57} + q^{59} + q^{60} + q^{64} + 2q^{68} + 2q^{71} - q^{76} - q^{79} - q^{80} - q^{81} + q^{84} - 2q^{85} + q^{87} + q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
59.1.b.a \(1\) \(0.029\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-59}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)

Hecke characteristic polynomials

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