Properties

Label 464.4.a.b
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

\(f(q)\) \(=\) \( q + 7 q^{3} - 15 q^{5} + 18 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 7 q^{3} - 15 q^{5} + 18 q^{7} + 22 q^{9} - 27 q^{11} - 57 q^{13} - 105 q^{15} - 44 q^{17} - 152 q^{19} + 126 q^{21} + 152 q^{23} + 100 q^{25} - 35 q^{27} - 29 q^{29} + 173 q^{31} - 189 q^{33} - 270 q^{35} - 120 q^{37} - 399 q^{39} - 314 q^{41} - 339 q^{43} - 330 q^{45} + 357 q^{47} - 19 q^{49} - 308 q^{51} - 59 q^{53} + 405 q^{55} - 1064 q^{57} + 572 q^{59} - 420 q^{61} + 396 q^{63} + 855 q^{65} - 660 q^{67} + 1064 q^{69} - 726 q^{71} + 1004 q^{73} + 700 q^{75} - 486 q^{77} - 361 q^{79} - 839 q^{81} + 168 q^{83} + 660 q^{85} - 203 q^{87} + 58 q^{89} - 1026 q^{91} + 1211 q^{93} + 2280 q^{95} - 1206 q^{97} - 594 q^{99}+O(q^{100}) \) 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 −15.0000 0 18.0000 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 464.4.a.b 1
4.b odd 2 1 58.4.a.b 1
8.b even 2 1 1856.4.a.c 1
8.d odd 2 1 1856.4.a.f 1
12.b even 2 1 522.4.a.b 1
20.d odd 2 1 1450.4.a.d 1
116.d odd 2 1 1682.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.4.a.b 1 4.b odd 2 1
464.4.a.b 1 1.a even 1 1 trivial
522.4.a.b 1 12.b even 2 1
1450.4.a.d 1 20.d odd 2 1
1682.4.a.a 1 116.d odd 2 1
1856.4.a.c 1 8.b even 2 1
1856.4.a.f 1 8.d odd 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
$5$ \( T + 15 \) Copy content Toggle raw display
$7$ \( T - 18 \) Copy content Toggle raw display
$11$ \( T + 27 \) Copy content Toggle raw display
$13$ \( T + 57 \) Copy content Toggle raw display
$17$ \( T + 44 \) Copy content Toggle raw display
$19$ \( T + 152 \) Copy content Toggle raw display
$23$ \( T - 152 \) Copy content Toggle raw display
$29$ \( T + 29 \) Copy content Toggle raw display
$31$ \( T - 173 \) Copy content Toggle raw display
$37$ \( T + 120 \) Copy content Toggle raw display
$41$ \( T + 314 \) Copy content Toggle raw display
$43$ \( T + 339 \) Copy content Toggle raw display
$47$ \( T - 357 \) Copy content Toggle raw display
$53$ \( T + 59 \) Copy content Toggle raw display
$59$ \( T - 572 \) Copy content Toggle raw display
$61$ \( T + 420 \) Copy content Toggle raw display
$67$ \( T + 660 \) Copy content Toggle raw display
$71$ \( T + 726 \) Copy content Toggle raw display
$73$ \( T - 1004 \) Copy content Toggle raw display
$79$ \( T + 361 \) Copy content Toggle raw display
$83$ \( T - 168 \) Copy content Toggle raw display
$89$ \( T - 58 \) Copy content Toggle raw display
$97$ \( T + 1206 \) Copy content Toggle raw display
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