Properties

Label 8550.2.a.bh
Level $8550$
Weight $2$
Character orbit 8550.a
Self dual yes
Analytic conductor $68.272$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8550.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(68.2720937282\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 2q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + 2q^{7} + q^{8} - 6q^{13} + 2q^{14} + q^{16} + 8q^{17} + q^{19} - 4q^{23} - 6q^{26} + 2q^{28} - 2q^{29} - 2q^{31} + q^{32} + 8q^{34} + 2q^{37} + q^{38} + 12q^{41} - 4q^{43} - 4q^{46} + 12q^{47} - 3q^{49} - 6q^{52} + 10q^{53} + 2q^{56} - 2q^{58} - 6q^{59} - 14q^{61} - 2q^{62} + q^{64} + 12q^{67} + 8q^{68} + 8q^{71} + 10q^{73} + 2q^{74} + q^{76} + 14q^{79} + 12q^{82} + 2q^{83} - 4q^{86} - 12q^{91} - 4q^{92} + 12q^{94} - 2q^{97} - 3q^{98} + O(q^{100}) \)

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
1.00000 0 1.00000 0 0 2.00000 1.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

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 8550.2.a.bh 1
3.b odd 2 1 2850.2.a.n 1
5.b even 2 1 1710.2.a.c 1
15.d odd 2 1 570.2.a.h 1
15.e even 4 2 2850.2.d.e 2
60.h even 2 1 4560.2.a.bc 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
570.2.a.h 1 15.d odd 2 1
1710.2.a.c 1 5.b even 2 1
2850.2.a.n 1 3.b odd 2 1
2850.2.d.e 2 15.e even 4 2
4560.2.a.bc 1 60.h even 2 1
8550.2.a.bh 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\):

\( T_{7} - 2 \)
\( T_{11} \)
\( T_{13} + 6 \)
\( T_{17} - 8 \)
\( T_{23} + 4 \)
\( T_{53} - 10 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -2 + T \)
$11$ \( T \)
$13$ \( 6 + T \)
$17$ \( -8 + T \)
$19$ \( -1 + T \)
$23$ \( 4 + T \)
$29$ \( 2 + T \)
$31$ \( 2 + T \)
$37$ \( -2 + T \)
$41$ \( -12 + T \)
$43$ \( 4 + T \)
$47$ \( -12 + T \)
$53$ \( -10 + T \)
$59$ \( 6 + T \)
$61$ \( 14 + T \)
$67$ \( -12 + T \)
$71$ \( -8 + T \)
$73$ \( -10 + T \)
$79$ \( -14 + T \)
$83$ \( -2 + T \)
$89$ \( T \)
$97$ \( 2 + T \)
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