Properties

Label 8550.2.a.e
Level $8550$
Weight $2$
Character orbit 8550.a
Self dual yes
Analytic conductor $68.272$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 2q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - 2q^{7} - q^{8} - 2q^{13} + 2q^{14} + q^{16} + q^{19} + 2q^{26} - 2q^{28} + 6q^{29} + 2q^{31} - q^{32} - 2q^{37} - q^{38} - 8q^{43} - 3q^{49} - 2q^{52} + 6q^{53} + 2q^{56} - 6q^{58} + 6q^{59} + 2q^{61} - 2q^{62} + q^{64} + 4q^{67} - 14q^{73} + 2q^{74} + q^{76} + 2q^{79} + 6q^{83} + 8q^{86} + 12q^{89} + 4q^{91} + 10q^{97} + 3q^{98} + O(q^{100}) \)

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.e 1
3.b odd 2 1 2850.2.a.q 1
5.b even 2 1 1710.2.a.o 1
15.d odd 2 1 570.2.a.f 1
15.e even 4 2 2850.2.d.d 2
60.h even 2 1 4560.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
570.2.a.f 1 15.d odd 2 1
1710.2.a.o 1 5.b even 2 1
2850.2.a.q 1 3.b odd 2 1
2850.2.d.d 2 15.e even 4 2
4560.2.a.m 1 60.h even 2 1
8550.2.a.e 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\):

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

Hecke characteristic polynomials

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