Properties

Label 64.20.a.b
Level $64$
Weight $20$
Character orbit 64.a
Self dual yes
Analytic conductor $146.443$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 64.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(146.442685796\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 50652 q^{3} + 2377410 q^{5} - 16917544 q^{7} + 1403363637 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 50652 q^{3} + 2377410 q^{5} - 16917544 q^{7} + 1403363637 q^{9} + 16212108 q^{11} - 50421615062 q^{13} - 120420571320 q^{15} + 225070099506 q^{17} + 1710278572660 q^{19} + 856907438688 q^{21} + 14036534788872 q^{23} - 13421408020025 q^{25} - 12212307114840 q^{27} - 1137835269510 q^{29} - 104626880141728 q^{31} - 821175694416 q^{33} - 40219938281040 q^{35} + 169392327370594 q^{37} + 25\!\cdots\!24 q^{39}+ \cdots + 22\!\cdots\!96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 −50652.0 0 2.37741e6 0 −1.69175e7 0 1.40336e9 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 64.20.a.b 1
4.b odd 2 1 64.20.a.h 1
8.b even 2 1 1.20.a.a 1
8.d odd 2 1 16.20.a.a 1
24.h odd 2 1 9.20.a.a 1
40.f even 2 1 25.20.a.a 1
40.i odd 4 2 25.20.b.a 2
56.h odd 2 1 49.20.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.20.a.a 1 8.b even 2 1
9.20.a.a 1 24.h odd 2 1
16.20.a.a 1 8.d odd 2 1
25.20.a.a 1 40.f even 2 1
25.20.b.a 2 40.i odd 4 2
49.20.a.b 1 56.h odd 2 1
64.20.a.b 1 1.a even 1 1 trivial
64.20.a.h 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 50652 \) acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(64))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 50652 \) Copy content Toggle raw display
$5$ \( T - 2377410 \) Copy content Toggle raw display
$7$ \( T + 16917544 \) Copy content Toggle raw display
$11$ \( T - 16212108 \) Copy content Toggle raw display
$13$ \( T + 50421615062 \) Copy content Toggle raw display
$17$ \( T - 225070099506 \) Copy content Toggle raw display
$19$ \( T - 1710278572660 \) Copy content Toggle raw display
$23$ \( T - 14036534788872 \) Copy content Toggle raw display
$29$ \( T + 1137835269510 \) Copy content Toggle raw display
$31$ \( T + 104626880141728 \) Copy content Toggle raw display
$37$ \( T - 169392327370594 \) Copy content Toggle raw display
$41$ \( T + 3309984750560838 \) Copy content Toggle raw display
$43$ \( T + 1127913532193492 \) Copy content Toggle raw display
$47$ \( T - 3498693987674256 \) Copy content Toggle raw display
$53$ \( T + 29\!\cdots\!02 \) Copy content Toggle raw display
$59$ \( T + 58\!\cdots\!20 \) Copy content Toggle raw display
$61$ \( T + 23\!\cdots\!42 \) Copy content Toggle raw display
$67$ \( T - 20\!\cdots\!44 \) Copy content Toggle raw display
$71$ \( T + 17\!\cdots\!68 \) Copy content Toggle raw display
$73$ \( T - 29\!\cdots\!22 \) Copy content Toggle raw display
$79$ \( T + 92\!\cdots\!40 \) Copy content Toggle raw display
$83$ \( T + 12\!\cdots\!32 \) Copy content Toggle raw display
$89$ \( T - 43\!\cdots\!30 \) Copy content Toggle raw display
$97$ \( T + 63\!\cdots\!94 \) Copy content Toggle raw display
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