Properties

Label 576.4.a.i
Level $576$
Weight $4$
Character orbit 576.a
Self dual yes
Analytic conductor $33.985$
Analytic rank $1$
Dimension $1$
CM discriminant -4
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.9851001633\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 288)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q - 4 q^{5} - 18 q^{13} + 104 q^{17} - 109 q^{25} - 284 q^{29} - 214 q^{37} + 472 q^{41} - 343 q^{49} - 572 q^{53} - 830 q^{61} + 72 q^{65} - 1098 q^{73} - 416 q^{85} - 176 q^{89} - 594 q^{97}+O(q^{100}) \) 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 0 0 −4.00000 0 0 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 CM by \(\Q(\sqrt{-1}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 576.4.a.i 1
3.b odd 2 1 576.4.a.p 1
4.b odd 2 1 CM 576.4.a.i 1
8.b even 2 1 288.4.a.g yes 1
8.d odd 2 1 288.4.a.g yes 1
12.b even 2 1 576.4.a.p 1
24.f even 2 1 288.4.a.d 1
24.h odd 2 1 288.4.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
288.4.a.d 1 24.f even 2 1
288.4.a.d 1 24.h odd 2 1
288.4.a.g yes 1 8.b even 2 1
288.4.a.g yes 1 8.d odd 2 1
576.4.a.i 1 1.a even 1 1 trivial
576.4.a.i 1 4.b odd 2 1 CM
576.4.a.p 1 3.b odd 2 1
576.4.a.p 1 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(576))\):

\( T_{5} + 4 \) Copy content Toggle raw display
\( T_{7} \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T + 4 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T + 18 \) Copy content Toggle raw display
$17$ \( T - 104 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 284 \) Copy content Toggle raw display
$31$ \( T \) Copy content Toggle raw display
$37$ \( T + 214 \) Copy content Toggle raw display
$41$ \( T - 472 \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T + 572 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T + 830 \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T + 1098 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T + 176 \) Copy content Toggle raw display
$97$ \( T + 594 \) Copy content Toggle raw display
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