Properties

Label 43.9
Level 43
Weight 9
Dimension 595
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 1386
Trace bound 1

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Defining parameters

Level: \( N \) = \( 43\( 43 \) \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(1386\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(43))\).

Total New Old
Modular forms 637 637 0
Cusp forms 595 595 0
Eisenstein series 42 42 0

Trace form

\( 595q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10}) \) \( 595q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} + 7082516q^{31} - 11370261q^{32} - 11073531q^{33} + 4628715q^{34} + 12403545q^{35} + 31352811q^{36} + 3467709q^{37} - 14353941q^{38} - 17435838q^{39} - 65780757q^{40} - 5441520q^{41} + 31478454q^{43} + 44932566q^{44} + 64068144q^{45} + 39427563q^{46} + 2485014q^{47} - 60963861q^{48} - 40353628q^{49} - 89607189q^{50} - 37792839q^{51} - 24156181q^{52} + 37373469q^{53} + 123451755q^{54} + 82757745q^{55} - 38723349q^{56} - 67867086q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} + 349060971q^{69} - 275782521q^{70} - 227534853q^{71} - 664959771q^{72} + 10739211q^{73} + 446325936q^{74} + 643124979q^{75} + 611597742q^{76} + 340925739q^{77} + 147018942q^{78} - 147694197q^{79} - 615195021q^{80} - 803929749q^{81} - 1032844071q^{82} - 339274677q^{83} - 869681547q^{84} + 415090851q^{86} + 982606758q^{87} + 1043761971q^{88} + 566201643q^{89} + 2292333729q^{90} + 349818315q^{91} + 257389629q^{92} - 395818773q^{93} - 1006781853q^{94} - 752220021q^{95} - 2855135304q^{96} - 1233640821q^{97} - 953460984q^{98} - 80665389q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(43))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
43.9.b \(\chi_{43}(42, \cdot)\) 43.9.b.a 1 1
43.9.b.b 28
43.9.d \(\chi_{43}(7, \cdot)\) 43.9.d.a 56 2
43.9.f \(\chi_{43}(2, \cdot)\) 43.9.f.a 174 6
43.9.h \(\chi_{43}(3, \cdot)\) 43.9.h.a 336 12

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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