Properties

Label 9.5.b
Level 9
Weight 5
Character orbit b
Rep. character \(\chi_{9}(8,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 9.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(9, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 4q^{4} - 56q^{7} + O(q^{10}) \) \( 2q - 4q^{4} - 56q^{7} + 252q^{10} - 224q^{13} - 568q^{16} + 1120q^{19} - 144q^{22} - 514q^{25} + 112q^{28} - 728q^{31} + 756q^{34} - 1652q^{37} + 3528q^{40} + 3472q^{43} - 6768q^{46} - 3234q^{49} + 448q^{52} + 1008q^{55} + 8388q^{58} + 5236q^{61} - 6928q^{64} - 7568q^{67} - 7056q^{70} + 13216q^{73} - 2240q^{76} - 8552q^{79} + 15372q^{82} - 5292q^{85} - 2016q^{88} + 6272q^{91} + 11088q^{94} - 11648q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.5.b.a \(2\) \(0.930\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 14 T^{2} + 256 T^{4} \)
$3$ 1
$5$ \( 1 - 368 T^{2} + 390625 T^{4} \)
$7$ \( ( 1 + 28 T + 2401 T^{2} )^{2} \)
$11$ \( 1 - 28994 T^{2} + 214358881 T^{4} \)
$13$ \( ( 1 + 112 T + 28561 T^{2} )^{2} \)
$17$ \( 1 - 159104 T^{2} + 6975757441 T^{4} \)
$19$ \( ( 1 - 560 T + 130321 T^{2} )^{2} \)
$23$ \( 1 + 76510 T^{2} + 78310985281 T^{4} \)
$29$ \( 1 - 437360 T^{2} + 500246412961 T^{4} \)
$31$ \( ( 1 + 364 T + 923521 T^{2} )^{2} \)
$37$ \( ( 1 + 826 T + 1874161 T^{2} )^{2} \)
$41$ \( 1 - 2369600 T^{2} + 7984925229121 T^{4} \)
$43$ \( ( 1 - 1736 T + 3418801 T^{2} )^{2} \)
$47$ \( 1 - 8051810 T^{2} + 23811286661761 T^{4} \)
$53$ \( 1 - 12560240 T^{2} + 62259690411361 T^{4} \)
$59$ \( 1 - 3856994 T^{2} + 146830437604321 T^{4} \)
$61$ \( ( 1 - 2618 T + 13845841 T^{2} )^{2} \)
$67$ \( ( 1 + 3784 T + 20151121 T^{2} )^{2} \)
$71$ \( 1 + 23206750 T^{2} + 645753531245761 T^{4} \)
$73$ \( ( 1 - 6608 T + 28398241 T^{2} )^{2} \)
$79$ \( ( 1 + 4276 T + 38950081 T^{2} )^{2} \)
$83$ \( 1 - 94902530 T^{2} + 2252292232139041 T^{4} \)
$89$ \( 1 - 106425344 T^{2} + 3936588805702081 T^{4} \)
$97$ \( ( 1 + 5824 T + 88529281 T^{2} )^{2} \)
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