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Properties

Label 17.2.a
Level 17
Weight 2
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(17))\).

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 the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(17\)Dim.
\(-\)\(1\)

Trace form

\( q - q^{2} - q^{4} - 2q^{5} + 4q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2q^{5} + 4q^{7} + 3q^{8} - 3q^{9} + 2q^{10} - 2q^{13} - 4q^{14} - q^{16} + q^{17} + 3q^{18} - 4q^{19} + 2q^{20} + 4q^{23} - q^{25} + 2q^{26} - 4q^{28} + 6q^{29} + 4q^{31} - 5q^{32} - q^{34} - 8q^{35} + 3q^{36} - 2q^{37} + 4q^{38} - 6q^{40} - 6q^{41} + 4q^{43} + 6q^{45} - 4q^{46} + 9q^{49} + q^{50} + 2q^{52} + 6q^{53} + 12q^{56} - 6q^{58} - 12q^{59} - 10q^{61} - 4q^{62} - 12q^{63} + 7q^{64} + 4q^{65} + 4q^{67} - q^{68} + 8q^{70} - 4q^{71} - 9q^{72} - 6q^{73} + 2q^{74} + 4q^{76} + 12q^{79} + 2q^{80} + 9q^{81} + 6q^{82} - 4q^{83} - 2q^{85} - 4q^{86} + 10q^{89} - 6q^{90} - 8q^{91} - 4q^{92} + 8q^{95} + 2q^{97} - 9q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.2.a.a \(1\) \(0.136\) \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) \(-\) \(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + 2 T^{2} \)
$3$ \( 1 + 3 T^{2} \)
$5$ \( 1 + 2 T + 5 T^{2} \)
$7$ \( 1 - 4 T + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - T \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 - 4 T + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 - 4 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 + 6 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 + 10 T + 61 T^{2} \)
$67$ \( 1 - 4 T + 67 T^{2} \)
$71$ \( 1 + 4 T + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 - 12 T + 79 T^{2} \)
$83$ \( 1 + 4 T + 83 T^{2} \)
$89$ \( 1 - 10 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
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