Properties

Label 43.7.b.a
Level $43$
Weight $7$
Character orbit 43.b
Self dual yes
Analytic conductor $9.892$
Analytic rank $0$
Dimension $1$
CM discriminant -43
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(9.89232559565\)
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

\(f(q)\) \(=\) \( q + 64q^{4} + 729q^{9} + O(q^{10}) \) \( q + 64q^{4} + 729q^{9} - 1638q^{11} + 3706q^{13} + 4096q^{16} + 7074q^{17} - 4734q^{23} + 15625q^{25} - 47918q^{31} + 46656q^{36} - 137358q^{41} - 79507q^{43} - 104832q^{44} + 42354q^{47} + 117649q^{49} + 237184q^{52} - 280854q^{53} + 406458q^{59} + 262144q^{64} - 471926q^{67} + 452736q^{68} + 259378q^{79} + 531441q^{81} - 681174q^{83} - 302976q^{92} - 1741246q^{97} - 1194102q^{99} + O(q^{100}) \)

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 64.0000 0 0 0 0 729.000 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 43.7.b.a 1
43.b odd 2 1 CM 43.7.b.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.7.b.a 1 1.a even 1 1 trivial
43.7.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 \(S_{7}^{\mathrm{new}}(43, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( 1638 + T \)
$13$ \( -3706 + T \)
$17$ \( -7074 + T \)
$19$ \( T \)
$23$ \( 4734 + T \)
$29$ \( T \)
$31$ \( 47918 + T \)
$37$ \( T \)
$41$ \( 137358 + T \)
$43$ \( 79507 + T \)
$47$ \( -42354 + T \)
$53$ \( 280854 + T \)
$59$ \( -406458 + T \)
$61$ \( T \)
$67$ \( 471926 + T \)
$71$ \( T \)
$73$ \( T \)
$79$ \( -259378 + T \)
$83$ \( 681174 + T \)
$89$ \( T \)
$97$ \( 1741246 + T \)
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