Properties

Label 43.11.b.a
Level 43
Weight 11
Character orbit 43.b
Self dual yes
Analytic conductor 27.320
Analytic rank 0
Dimension 1
CM discriminant -43
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q + 1024q^{4} + 59049q^{9} + O(q^{10}) \) \( q + 1024q^{4} + 59049q^{9} - 18501q^{11} + 303943q^{13} + 1048576q^{16} - 2764089q^{17} + 4126443q^{23} + 9765625q^{25} + 57253099q^{31} + 60466176q^{36} + 142671399q^{41} - 147008443q^{43} - 18945024q^{44} + 451176882q^{47} + 282475249q^{49} + 311237632q^{52} - 33972057q^{53} - 990191574q^{59} + 1073741824q^{64} - 1504819589q^{67} - 2830427136q^{68} - 2641416974q^{79} + 3486784401q^{81} - 6757639557q^{83} + 4225477632q^{92} - 15006753793q^{97} - 1092465549q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
42.1
0
0 0 1024.00 0 0 0 0 59049.0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 CM by \(\Q(\sqrt{-43}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.11.b.a 1
43.b odd 2 1 CM 43.11.b.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.11.b.a 1 1.a even 1 1 trivial
43.11.b.a 1 43.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{11}^{\mathrm{new}}(43, [\chi])\).

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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