Properties

Label 43.11.b
Level 43
Weight 11
Character orbit b
Rep. character \(\chi_{43}(42,\cdot)\)
Character field \(\Q\)
Dimension 35
Newform subspaces 2
Sturm bound 40
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
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: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(43, [\chi])\).

Total New Old
Modular forms 37 37 0
Cusp forms 35 35 0
Eisenstein series 2 2 0

Trace form

\( 35q - 15132q^{4} + 12798q^{6} - 731667q^{9} + O(q^{10}) \) \( 35q - 15132q^{4} + 12798q^{6} - 731667q^{9} - 254122q^{10} - 236701q^{11} + 112935q^{13} - 1380228q^{14} - 512732q^{15} + 3272884q^{16} - 3834767q^{17} + 17857352q^{21} + 13041697q^{23} - 39666730q^{24} - 73172659q^{25} + 2210689q^{31} - 179227232q^{35} + 454847218q^{36} + 709061882q^{38} + 433255366q^{40} + 223042025q^{41} - 145423381q^{43} + 305532864q^{44} - 93733620q^{47} - 2196870673q^{49} - 675821820q^{52} - 949858877q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 2404625190q^{59} - 5474941192q^{60} + 3999067300q^{64} + 455136192q^{66} + 1901100799q^{67} - 2166418910q^{68} + 16264108918q^{74} - 17800086268q^{78} - 16494567832q^{79} + 23931485947q^{81} - 6643772321q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 45649260690q^{92} + 4107406010q^{95} + 33148445474q^{96} + 788363361q^{97} + 253412051q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.11.b.a \(1\) \(27.320\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{10}q^{4}+3^{10}q^{9}-18501q^{11}+\cdots\)
43.11.b.b \(34\) \(27.320\) None \(0\) \(0\) \(0\) \(0\)

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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