Properties

Label 8550.2.a.c
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 2850)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 4q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - 4q^{7} - q^{8} + q^{11} + 4q^{14} + q^{16} + 8q^{17} + q^{19} - q^{22} + 3q^{23} - 4q^{28} + q^{29} + q^{31} - q^{32} - 8q^{34} - 2q^{37} - q^{38} + 10q^{41} - 8q^{43} + q^{44} - 3q^{46} + 9q^{49} - 3q^{53} + 4q^{56} - q^{58} - 4q^{59} + 5q^{61} - q^{62} + q^{64} - 5q^{67} + 8q^{68} + 6q^{71} - 13q^{73} + 2q^{74} + q^{76} - 4q^{77} - 5q^{79} - 10q^{82} - 11q^{83} + 8q^{86} - q^{88} - 3q^{89} + 3q^{92} + 10q^{97} - 9q^{98} + O(q^{100}) \)

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 −4.00000 −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.c 1
3.b odd 2 1 2850.2.a.w yes 1
5.b even 2 1 8550.2.a.bk 1
15.d odd 2 1 2850.2.a.f 1
15.e even 4 2 2850.2.d.o 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2850.2.a.f 1 15.d odd 2 1
2850.2.a.w yes 1 3.b odd 2 1
2850.2.d.o 2 15.e even 4 2
8550.2.a.c 1 1.a even 1 1 trivial
8550.2.a.bk 1 5.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\):

\( T_{7} + 4 \)
\( T_{11} - 1 \)
\( T_{13} \)
\( T_{17} - 8 \)
\( T_{23} - 3 \)
\( T_{53} + 3 \)

Hecke characteristic polynomials

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