Properties

Label 8550.2.a.bd
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 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{7} + q^{8} + q^{13} + q^{14} + q^{16} - 3q^{17} + q^{19} + 3q^{23} + q^{26} + q^{28} + 3q^{29} + 2q^{31} + q^{32} - 3q^{34} + 10q^{37} + q^{38} - 6q^{41} - 2q^{43} + 3q^{46} - 6q^{49} + q^{52} + 3q^{53} + q^{56} + 3q^{58} - 3q^{59} + 8q^{61} + 2q^{62} + q^{64} + 7q^{67} - 3q^{68} - 12q^{71} + 13q^{73} + 10q^{74} + q^{76} + 14q^{79} - 6q^{82} + 6q^{83} - 2q^{86} - 6q^{89} + q^{91} + 3q^{92} + 10q^{97} - 6q^{98} + O(q^{100}) \)

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 1.00000 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.bd 1
3.b odd 2 1 950.2.a.a 1
5.b even 2 1 1710.2.a.d 1
12.b even 2 1 7600.2.a.m 1
15.d odd 2 1 190.2.a.c 1
15.e even 4 2 950.2.b.e 2
60.h even 2 1 1520.2.a.d 1
105.g even 2 1 9310.2.a.o 1
120.i odd 2 1 6080.2.a.h 1
120.m even 2 1 6080.2.a.p 1
285.b even 2 1 3610.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.c 1 15.d odd 2 1
950.2.a.a 1 3.b odd 2 1
950.2.b.e 2 15.e even 4 2
1520.2.a.d 1 60.h even 2 1
1710.2.a.d 1 5.b even 2 1
3610.2.a.b 1 285.b even 2 1
6080.2.a.h 1 120.i odd 2 1
6080.2.a.p 1 120.m even 2 1
7600.2.a.m 1 12.b even 2 1
8550.2.a.bd 1 1.a even 1 1 trivial
9310.2.a.o 1 105.g even 2 1

Hecke kernels

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

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

Hecke characteristic polynomials

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