Properties

Label 43.9.b
Level 43
Weight 9
Character orbit b
Rep. character \(\chi_{43}(42,\cdot)\)
Character field \(\Q\)
Dimension 29
Newform subspaces 2
Sturm bound 33
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(33\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(43, [\chi])\).

Total New Old
Modular forms 31 31 0
Cusp forms 29 29 0
Eisenstein series 2 2 0

Trace form

\( 29q - 4028q^{4} - 1794q^{6} - 74193q^{9} + O(q^{10}) \) \( 29q - 4028q^{4} - 1794q^{6} - 74193q^{9} + 24982q^{10} + 14857q^{11} - 32635q^{13} + 24732q^{14} + 15388q^{15} + 591348q^{16} - 55169q^{17} - 261352q^{21} + 356287q^{23} + 1770326q^{24} - 2249809q^{25} + 479407q^{31} + 10947816q^{35} + 13281682q^{36} - 7189158q^{38} - 21389338q^{40} - 960905q^{41} + 5892221q^{43} - 6176816q^{44} - 5000240q^{47} - 9796135q^{49} - 1080700q^{52} + 10880833q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 13418942q^{59} - 44902072q^{60} - 153667356q^{64} - 48457584q^{66} - 170770235q^{67} + 170492674q^{68} + 205870278q^{74} + 267860612q^{78} + 80425884q^{79} - 14554283q^{81} - 135695411q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 271107950q^{92} + 123322986q^{95} - 692987086q^{96} - 156101641q^{97} - 542004247q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.9.b.a \(1\) \(17.517\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots\)
43.9.b.b \(28\) \(17.517\) None \(0\) \(0\) \(0\) \(0\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 16 T )( 1 + 16 T ) \))
$3$ (\( ( 1 - 81 T )( 1 + 81 T ) \))
$5$ (\( ( 1 - 625 T )( 1 + 625 T ) \))
$7$ (\( ( 1 - 2401 T )( 1 + 2401 T ) \))
$11$ (\( 1 - 10319 T + 214358881 T^{2} \))
$13$ (\( 1 + 54721 T + 815730721 T^{2} \))
$17$ (\( 1 - 79967 T + 6975757441 T^{2} \))
$19$ (\( ( 1 - 130321 T )( 1 + 130321 T ) \))
$23$ (\( 1 - 540719 T + 78310985281 T^{2} \))
$29$ (\( ( 1 - 707281 T )( 1 + 707281 T ) \))
$31$ (\( 1 - 589679 T + 852891037441 T^{2} \))
$37$ (\( ( 1 - 1874161 T )( 1 + 1874161 T ) \))
$41$ (\( 1 + 2262241 T + 7984925229121 T^{2} \))
$43$ (\( 1 - 3418801 T \))
$47$ (\( 1 + 6983806 T + 23811286661761 T^{2} \))
$53$ (\( 1 + 13061761 T + 62259690411361 T^{2} \))
$59$ (\( 1 + 7864606 T + 146830437604321 T^{2} \))
$61$ (\( ( 1 - 13845841 T )( 1 + 13845841 T ) \))
$67$ (\( 1 + 39816433 T + 406067677556641 T^{2} \))
$71$ (\( ( 1 - 25411681 T )( 1 + 25411681 T ) \))
$73$ (\( ( 1 - 28398241 T )( 1 + 28398241 T ) \))
$79$ (\( 1 - 73045634 T + 1517108809906561 T^{2} \))
$83$ (\( 1 + 93091441 T + 2252292232139041 T^{2} \))
$89$ (\( ( 1 - 62742241 T )( 1 + 62742241 T ) \))
$97$ (\( 1 - 162643199 T + 7837433594376961 T^{2} \))
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