Properties

Label 79.1.b
Level 79
Weight 1
Character orbit b
Rep. character \(\chi_{79}(78,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 79.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(79, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{8} + 2q^{9} - 2q^{10} - q^{11} - q^{13} - q^{18} - q^{19} + 2q^{20} + 3q^{22} - q^{23} + q^{25} + 3q^{26} - q^{31} + 2q^{32} + q^{36} - 2q^{38} + q^{40} - 3q^{44} - q^{45} - 2q^{46} + 2q^{49} + 2q^{50} - 3q^{52} - 2q^{55} + 3q^{62} - q^{64} - 2q^{65} - q^{67} - 2q^{72} - q^{73} + 2q^{76} + 2q^{79} + 2q^{81} + 4q^{83} + q^{88} - q^{89} - 2q^{90} + 2q^{92} + 3q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(79, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
79.1.b.a \(2\) \(0.039\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-79}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)

Hecke characteristic polynomials

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