Properties

Label 720.4.a.y
Level $720$
Weight $4$
Character orbit 720.a
Self dual yes
Analytic conductor $42.481$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.4813752041\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 5 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 5 q^{5} + 4 q^{7} - 48 q^{11} + 2 q^{13} + 114 q^{17} - 140 q^{19} + 72 q^{23} + 25 q^{25} - 210 q^{29} - 272 q^{31} + 20 q^{35} - 334 q^{37} + 198 q^{41} + 268 q^{43} + 216 q^{47} - 327 q^{49} + 78 q^{53} - 240 q^{55} + 240 q^{59} + 302 q^{61} + 10 q^{65} - 596 q^{67} - 768 q^{71} - 478 q^{73} - 192 q^{77} + 640 q^{79} - 348 q^{83} + 570 q^{85} - 210 q^{89} + 8 q^{91} - 700 q^{95} - 1534 q^{97}+O(q^{100}) \) 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 5.00000 0 4.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)

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 720.4.a.y 1
3.b odd 2 1 240.4.a.b 1
4.b odd 2 1 90.4.a.c 1
12.b even 2 1 30.4.a.b 1
15.d odd 2 1 1200.4.a.ba 1
15.e even 4 2 1200.4.f.r 2
20.d odd 2 1 450.4.a.r 1
20.e even 4 2 450.4.c.j 2
24.f even 2 1 960.4.a.n 1
24.h odd 2 1 960.4.a.bg 1
36.f odd 6 2 810.4.e.p 2
36.h even 6 2 810.4.e.i 2
60.h even 2 1 150.4.a.b 1
60.l odd 4 2 150.4.c.c 2
84.h odd 2 1 1470.4.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
30.4.a.b 1 12.b even 2 1
90.4.a.c 1 4.b odd 2 1
150.4.a.b 1 60.h even 2 1
150.4.c.c 2 60.l odd 4 2
240.4.a.b 1 3.b odd 2 1
450.4.a.r 1 20.d odd 2 1
450.4.c.j 2 20.e even 4 2
720.4.a.y 1 1.a even 1 1 trivial
810.4.e.i 2 36.h even 6 2
810.4.e.p 2 36.f odd 6 2
960.4.a.n 1 24.f even 2 1
960.4.a.bg 1 24.h odd 2 1
1200.4.a.ba 1 15.d odd 2 1
1200.4.f.r 2 15.e even 4 2
1470.4.a.r 1 84.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(720))\):

\( T_{7} - 4 \) Copy content Toggle raw display
\( T_{11} + 48 \) 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
$5$ \( T - 5 \) Copy content Toggle raw display
$7$ \( T - 4 \) Copy content Toggle raw display
$11$ \( T + 48 \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T - 114 \) Copy content Toggle raw display
$19$ \( T + 140 \) Copy content Toggle raw display
$23$ \( T - 72 \) Copy content Toggle raw display
$29$ \( T + 210 \) Copy content Toggle raw display
$31$ \( T + 272 \) Copy content Toggle raw display
$37$ \( T + 334 \) Copy content Toggle raw display
$41$ \( T - 198 \) Copy content Toggle raw display
$43$ \( T - 268 \) Copy content Toggle raw display
$47$ \( T - 216 \) Copy content Toggle raw display
$53$ \( T - 78 \) Copy content Toggle raw display
$59$ \( T - 240 \) Copy content Toggle raw display
$61$ \( T - 302 \) Copy content Toggle raw display
$67$ \( T + 596 \) Copy content Toggle raw display
$71$ \( T + 768 \) Copy content Toggle raw display
$73$ \( T + 478 \) Copy content Toggle raw display
$79$ \( T - 640 \) Copy content Toggle raw display
$83$ \( T + 348 \) Copy content Toggle raw display
$89$ \( T + 210 \) Copy content Toggle raw display
$97$ \( T + 1534 \) Copy content Toggle raw display
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