Properties

Label 43.11
Level 43
Weight 11
Dimension 749
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 1694
Trace bound 1

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Defining parameters

Level: \( N \) = \( 43\( 43 \) \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(1694\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(43))\).

Total New Old
Modular forms 791 791 0
Cusp forms 749 749 0
Eisenstein series 42 42 0

Trace form

\( 749q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10}) \) \( 749q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} + 231397222q^{31} - 526310421q^{32} + 189556017q^{33} + 645676395q^{34} + 21882693q^{35} - 1128701973q^{36} - 466608471q^{37} - 184821525q^{38} + 478649472q^{39} + 2754318315q^{40} + 268492518q^{41} - 1631946876q^{43} - 2109069354q^{44} - 2296120386q^{45} - 394324245q^{46} + 420456204q^{47} + 6667702251q^{48} + 1977326722q^{49} + 1203138027q^{50} - 1330015323q^{51} - 8043929621q^{52} - 2792804343q^{53} + 872980395q^{54} + 5635860573q^{55} + 3975594987q^{56} - 4438376796q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} + 11873168139q^{69} - 37796062521q^{70} - 5988151449q^{71} + 47896433109q^{72} + 14280491715q^{73} + 29982422064q^{74} - 6316406271q^{75} - 37806829914q^{76} - 43658152293q^{77} - 78107330322q^{78} - 9167555901q^{79} + 19480124979q^{80} + 52319063307q^{81} + 86801715609q^{82} + 32561946291q^{83} + 89672623173q^{84} - 43837514973q^{86} - 99232333662q^{87} - 95683720461q^{88} - 42958811301q^{89} - 111515906271q^{90} + 3329711763q^{91} + 86699540109q^{92} + 120767123883q^{93} + 142635419619q^{94} + 60687374979q^{95} + 87168774672q^{96} - 36608212893q^{97} - 137141594520q^{98} - 197448646311q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(43))\)

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
43.11.b \(\chi_{43}(42, \cdot)\) 43.11.b.a 1 1
43.11.b.b 34
43.11.d \(\chi_{43}(7, \cdot)\) 43.11.d.a 72 2
43.11.f \(\chi_{43}(2, \cdot)\) 43.11.f.a 210 6
43.11.h \(\chi_{43}(3, \cdot)\) 43.11.h.a 432 12

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 32 T )( 1 + 32 T ) \))
$3$ (\( ( 1 - 243 T )( 1 + 243 T ) \))
$5$ (\( ( 1 - 3125 T )( 1 + 3125 T ) \))
$7$ (\( ( 1 - 16807 T )( 1 + 16807 T ) \))
$11$ (\( 1 + 18501 T + 25937424601 T^{2} \))
$13$ (\( 1 - 303943 T + 137858491849 T^{2} \))
$17$ (\( 1 + 2764089 T + 2015993900449 T^{2} \))
$19$ (\( ( 1 - 2476099 T )( 1 + 2476099 T ) \))
$23$ (\( 1 - 4126443 T + 41426511213649 T^{2} \))
$29$ (\( ( 1 - 20511149 T )( 1 + 20511149 T ) \))
$31$ (\( 1 - 57253099 T + 819628286980801 T^{2} \))
$37$ (\( ( 1 - 69343957 T )( 1 + 69343957 T ) \))
$41$ (\( 1 - 142671399 T + 13422659310152401 T^{2} \))
$43$ (\( 1 + 147008443 T \))
$47$ (\( 1 - 451176882 T + 52599132235830049 T^{2} \))
$53$ (\( 1 + 33972057 T + 174887470365513049 T^{2} \))
$59$ (\( 1 + 990191574 T + 511116753300641401 T^{2} \))
$61$ (\( ( 1 - 844596301 T )( 1 + 844596301 T ) \))
$67$ (\( 1 + 1504819589 T + 1822837804551761449 T^{2} \))
$71$ (\( ( 1 - 1804229351 T )( 1 + 1804229351 T ) \))
$73$ (\( ( 1 - 2073071593 T )( 1 + 2073071593 T ) \))
$79$ (\( 1 + 2641416974 T + 9468276082626847201 T^{2} \))
$83$ (\( 1 + 6757639557 T + 15516041187205853449 T^{2} \))
$89$ (\( ( 1 - 5584059449 T )( 1 + 5584059449 T ) \))
$97$ (\( 1 + 15006753793 T + 73742412689492826049 T^{2} \))
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