Properties

Label 464.4.a.a
Level $464$
Weight $4$
Character orbit 464.a
Self dual yes
Analytic conductor $27.377$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 464.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(27.3768862427\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 58)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 7 q^{3} + 5 q^{5} + 2 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 7 q^{3} + 5 q^{5} + 2 q^{7} + 22 q^{9} - 37 q^{11} + 27 q^{13} - 35 q^{15} + 24 q^{17} + 88 q^{19} - 14 q^{21} + 28 q^{23} - 100 q^{25} + 35 q^{27} - 29 q^{29} + 143 q^{31} + 259 q^{33} + 10 q^{35} - 360 q^{37} - 189 q^{39} + 386 q^{41} - 381 q^{43} + 110 q^{45} + 103 q^{47} - 339 q^{49} - 168 q^{51} - 431 q^{53} - 185 q^{55} - 616 q^{57} - 288 q^{59} - 840 q^{61} + 44 q^{63} + 135 q^{65} + 180 q^{67} - 196 q^{69} - 706 q^{71} + 716 q^{73} + 700 q^{75} - 74 q^{77} - 931 q^{79} - 839 q^{81} - 1188 q^{83} + 120 q^{85} + 203 q^{87} - 642 q^{89} + 54 q^{91} - 1001 q^{93} + 440 q^{95} + 486 q^{97} - 814 q^{99}+O(q^{100}) \) 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 5.00000 0 2.00000 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 464.4.a.a 1
4.b odd 2 1 58.4.a.a 1
8.b even 2 1 1856.4.a.d 1
8.d odd 2 1 1856.4.a.a 1
12.b even 2 1 522.4.a.e 1
20.d odd 2 1 1450.4.a.e 1
116.d odd 2 1 1682.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.4.a.a 1 4.b odd 2 1
464.4.a.a 1 1.a even 1 1 trivial
522.4.a.e 1 12.b even 2 1
1450.4.a.e 1 20.d odd 2 1
1682.4.a.b 1 116.d odd 2 1
1856.4.a.a 1 8.d odd 2 1
1856.4.a.d 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(464))\). 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
$5$ \( T - 5 \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T + 37 \) Copy content Toggle raw display
$13$ \( T - 27 \) Copy content Toggle raw display
$17$ \( T - 24 \) Copy content Toggle raw display
$19$ \( T - 88 \) Copy content Toggle raw display
$23$ \( T - 28 \) Copy content Toggle raw display
$29$ \( T + 29 \) Copy content Toggle raw display
$31$ \( T - 143 \) Copy content Toggle raw display
$37$ \( T + 360 \) Copy content Toggle raw display
$41$ \( T - 386 \) Copy content Toggle raw display
$43$ \( T + 381 \) Copy content Toggle raw display
$47$ \( T - 103 \) Copy content Toggle raw display
$53$ \( T + 431 \) Copy content Toggle raw display
$59$ \( T + 288 \) Copy content Toggle raw display
$61$ \( T + 840 \) Copy content Toggle raw display
$67$ \( T - 180 \) Copy content Toggle raw display
$71$ \( T + 706 \) Copy content Toggle raw display
$73$ \( T - 716 \) Copy content Toggle raw display
$79$ \( T + 931 \) Copy content Toggle raw display
$83$ \( T + 1188 \) Copy content Toggle raw display
$89$ \( T + 642 \) Copy content Toggle raw display
$97$ \( T - 486 \) Copy content Toggle raw display
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