Properties

Label 7200.2.a.bo
Level $7200$
Weight $2$
Character orbit 7200.a
Self dual yes
Analytic conductor $57.492$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(57.4922894553\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1440)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{7} + 2 q^{11} - 2 q^{17} - 4 q^{19} - 2 q^{29} - 8 q^{31} + 4 q^{37} + 8 q^{41} + 8 q^{43} + 8 q^{47} - 3 q^{49} + 10 q^{53} - 6 q^{59} + 2 q^{61} + 12 q^{67} + 12 q^{71} + 2 q^{73} + 4 q^{77} - 8 q^{79} + 4 q^{83} + 12 q^{89} - 10 q^{97}+O(q^{100}) \) 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 0 0 2.00000 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 7200.2.a.bo 1
3.b odd 2 1 7200.2.a.bn 1
4.b odd 2 1 7200.2.a.m 1
5.b even 2 1 1440.2.a.b 1
5.c odd 4 2 7200.2.f.v 2
12.b even 2 1 7200.2.a.n 1
15.d odd 2 1 1440.2.a.h yes 1
15.e even 4 2 7200.2.f.i 2
20.d odd 2 1 1440.2.a.e yes 1
20.e even 4 2 7200.2.f.h 2
40.e odd 2 1 2880.2.a.be 1
40.f even 2 1 2880.2.a.v 1
60.h even 2 1 1440.2.a.m yes 1
60.l odd 4 2 7200.2.f.u 2
120.i odd 2 1 2880.2.a.g 1
120.m even 2 1 2880.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1440.2.a.b 1 5.b even 2 1
1440.2.a.e yes 1 20.d odd 2 1
1440.2.a.h yes 1 15.d odd 2 1
1440.2.a.m yes 1 60.h even 2 1
2880.2.a.g 1 120.i odd 2 1
2880.2.a.l 1 120.m even 2 1
2880.2.a.v 1 40.f even 2 1
2880.2.a.be 1 40.e odd 2 1
7200.2.a.m 1 4.b odd 2 1
7200.2.a.n 1 12.b even 2 1
7200.2.a.bn 1 3.b odd 2 1
7200.2.a.bo 1 1.a even 1 1 trivial
7200.2.f.h 2 20.e even 4 2
7200.2.f.i 2 15.e even 4 2
7200.2.f.u 2 60.l odd 4 2
7200.2.f.v 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7200))\):

\( T_{7} - 2 \) Copy content Toggle raw display
\( T_{11} - 2 \) Copy content Toggle raw display
\( T_{13} \) Copy content Toggle raw display
\( T_{17} + 2 \) Copy content Toggle raw display
\( T_{19} + 4 \) Copy content Toggle raw display
\( T_{23} \) 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
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T + 2 \) Copy content Toggle raw display
$19$ \( T + 4 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T + 8 \) Copy content Toggle raw display
$37$ \( T - 4 \) Copy content Toggle raw display
$41$ \( T - 8 \) Copy content Toggle raw display
$43$ \( T - 8 \) Copy content Toggle raw display
$47$ \( T - 8 \) Copy content Toggle raw display
$53$ \( T - 10 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T - 12 \) Copy content Toggle raw display
$71$ \( T - 12 \) Copy content Toggle raw display
$73$ \( T - 2 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T - 12 \) Copy content Toggle raw display
$97$ \( T + 10 \) Copy content Toggle raw display
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