Properties

Label 8550.2.a.u
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 38)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 3q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - 3q^{7} + q^{8} - 2q^{11} + q^{13} - 3q^{14} + q^{16} + 3q^{17} - q^{19} - 2q^{22} - q^{23} + q^{26} - 3q^{28} + 5q^{29} - 8q^{31} + q^{32} + 3q^{34} + 2q^{37} - q^{38} + 8q^{41} - 4q^{43} - 2q^{44} - q^{46} + 8q^{47} + 2q^{49} + q^{52} - q^{53} - 3q^{56} + 5q^{58} - 15q^{59} + 2q^{61} - 8q^{62} + q^{64} - 3q^{67} + 3q^{68} - 2q^{71} - 9q^{73} + 2q^{74} - q^{76} + 6q^{77} - 10q^{79} + 8q^{82} - 6q^{83} - 4q^{86} - 2q^{88} - 3q^{91} - q^{92} + 8q^{94} + 2q^{97} + 2q^{98} + O(q^{100}) \)

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 −3.00000 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.u 1
3.b odd 2 1 950.2.a.b 1
5.b even 2 1 342.2.a.d 1
12.b even 2 1 7600.2.a.h 1
15.d odd 2 1 38.2.a.b 1
15.e even 4 2 950.2.b.c 2
20.d odd 2 1 2736.2.a.w 1
60.h even 2 1 304.2.a.d 1
95.d odd 2 1 6498.2.a.y 1
105.g even 2 1 1862.2.a.f 1
120.i odd 2 1 1216.2.a.n 1
120.m even 2 1 1216.2.a.g 1
165.d even 2 1 4598.2.a.a 1
195.e odd 2 1 6422.2.a.b 1
285.b even 2 1 722.2.a.b 1
285.n odd 6 2 722.2.c.d 2
285.q even 6 2 722.2.c.f 2
285.bd odd 18 6 722.2.e.c 6
285.bf even 18 6 722.2.e.d 6
1140.p odd 2 1 5776.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
38.2.a.b 1 15.d odd 2 1
304.2.a.d 1 60.h even 2 1
342.2.a.d 1 5.b even 2 1
722.2.a.b 1 285.b even 2 1
722.2.c.d 2 285.n odd 6 2
722.2.c.f 2 285.q even 6 2
722.2.e.c 6 285.bd odd 18 6
722.2.e.d 6 285.bf even 18 6
950.2.a.b 1 3.b odd 2 1
950.2.b.c 2 15.e even 4 2
1216.2.a.g 1 120.m even 2 1
1216.2.a.n 1 120.i odd 2 1
1862.2.a.f 1 105.g even 2 1
2736.2.a.w 1 20.d odd 2 1
4598.2.a.a 1 165.d even 2 1
5776.2.a.d 1 1140.p odd 2 1
6422.2.a.b 1 195.e odd 2 1
6498.2.a.y 1 95.d odd 2 1
7600.2.a.h 1 12.b even 2 1
8550.2.a.u 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\):

\( T_{7} + 3 \)
\( T_{11} + 2 \)
\( T_{13} - 1 \)
\( T_{17} - 3 \)
\( T_{23} + 1 \)
\( T_{53} + 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 3 + T \)
$11$ \( 2 + T \)
$13$ \( -1 + T \)
$17$ \( -3 + T \)
$19$ \( 1 + T \)
$23$ \( 1 + T \)
$29$ \( -5 + T \)
$31$ \( 8 + T \)
$37$ \( -2 + T \)
$41$ \( -8 + T \)
$43$ \( 4 + T \)
$47$ \( -8 + T \)
$53$ \( 1 + T \)
$59$ \( 15 + T \)
$61$ \( -2 + T \)
$67$ \( 3 + T \)
$71$ \( 2 + T \)
$73$ \( 9 + T \)
$79$ \( 10 + T \)
$83$ \( 6 + T \)
$89$ \( T \)
$97$ \( -2 + T \)
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