Properties

Label 928.4.a.a
Level $928$
Weight $4$
Character orbit 928.a
Self dual yes
Analytic conductor $54.754$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 928 = 2^{5} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 928.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.7537724853\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 7 q^{3} - 13 q^{5} + 16 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 7 q^{3} - 13 q^{5} + 16 q^{7} + 22 q^{9} - 45 q^{11} + 61 q^{13} + 91 q^{15} - 102 q^{17} - 68 q^{19} - 112 q^{21} + 194 q^{23} + 44 q^{25} + 35 q^{27} - 29 q^{29} + 149 q^{31} + 315 q^{33} - 208 q^{35} + 400 q^{37} - 427 q^{39} + 280 q^{41} + 263 q^{43} - 286 q^{45} + 509 q^{47} - 87 q^{49} + 714 q^{51} - 605 q^{53} + 585 q^{55} + 476 q^{57} - 578 q^{59} - 718 q^{61} + 352 q^{63} - 793 q^{65} - 260 q^{67} - 1358 q^{69} + 738 q^{71} + 652 q^{73} - 308 q^{75} - 720 q^{77} - 917 q^{79} - 839 q^{81} + 678 q^{83} + 1326 q^{85} + 203 q^{87} - 1008 q^{89} + 976 q^{91} - 1043 q^{93} + 884 q^{95} - 1764 q^{97} - 990 q^{99}+O(q^{100}) \) 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 −7.00000 0 −13.0000 0 16.0000 0 22.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(29\) \(1\)

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 928.4.a.a 1
4.b odd 2 1 928.4.a.b yes 1
8.b even 2 1 1856.4.a.e 1
8.d odd 2 1 1856.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
928.4.a.a 1 1.a even 1 1 trivial
928.4.a.b yes 1 4.b odd 2 1
1856.4.a.b 1 8.d odd 2 1
1856.4.a.e 1 8.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(928))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 7 \) Copy content Toggle raw display
$5$ \( T + 13 \) Copy content Toggle raw display
$7$ \( T - 16 \) Copy content Toggle raw display
$11$ \( T + 45 \) Copy content Toggle raw display
$13$ \( T - 61 \) Copy content Toggle raw display
$17$ \( T + 102 \) Copy content Toggle raw display
$19$ \( T + 68 \) Copy content Toggle raw display
$23$ \( T - 194 \) Copy content Toggle raw display
$29$ \( T + 29 \) Copy content Toggle raw display
$31$ \( T - 149 \) Copy content Toggle raw display
$37$ \( T - 400 \) Copy content Toggle raw display
$41$ \( T - 280 \) Copy content Toggle raw display
$43$ \( T - 263 \) Copy content Toggle raw display
$47$ \( T - 509 \) Copy content Toggle raw display
$53$ \( T + 605 \) Copy content Toggle raw display
$59$ \( T + 578 \) Copy content Toggle raw display
$61$ \( T + 718 \) Copy content Toggle raw display
$67$ \( T + 260 \) Copy content Toggle raw display
$71$ \( T - 738 \) Copy content Toggle raw display
$73$ \( T - 652 \) Copy content Toggle raw display
$79$ \( T + 917 \) Copy content Toggle raw display
$83$ \( T - 678 \) Copy content Toggle raw display
$89$ \( T + 1008 \) Copy content Toggle raw display
$97$ \( T + 1764 \) Copy content Toggle raw display
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