Properties

Label 8050.2.a.s
Level $8050$
Weight $2$
Character orbit 8050.a
Self dual yes
Analytic conductor $64.280$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8050 = 2 \cdot 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8050.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.2795736271\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} - 5q^{11} + q^{12} + 2q^{13} + q^{14} + q^{16} - 5q^{17} - 2q^{18} + 5q^{19} + q^{21} - 5q^{22} + q^{23} + q^{24} + 2q^{26} - 5q^{27} + q^{28} - 2q^{29} - 4q^{31} + q^{32} - 5q^{33} - 5q^{34} - 2q^{36} + 4q^{37} + 5q^{38} + 2q^{39} - 5q^{41} + q^{42} - 8q^{43} - 5q^{44} + q^{46} - 6q^{47} + q^{48} + q^{49} - 5q^{51} + 2q^{52} - 4q^{53} - 5q^{54} + q^{56} + 5q^{57} - 2q^{58} + 4q^{59} + 10q^{61} - 4q^{62} - 2q^{63} + q^{64} - 5q^{66} + q^{67} - 5q^{68} + q^{69} + 2q^{71} - 2q^{72} - 15q^{73} + 4q^{74} + 5q^{76} - 5q^{77} + 2q^{78} - 10q^{79} + q^{81} - 5q^{82} + 3q^{83} + q^{84} - 8q^{86} - 2q^{87} - 5q^{88} - 15q^{89} + 2q^{91} + q^{92} - 4q^{93} - 6q^{94} + q^{96} - 2q^{97} + q^{98} + 10q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(7\) \(-1\)
\(23\) \(-1\)

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 8050.2.a.s yes 1
5.b even 2 1 8050.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8050.2.a.c 1 5.b even 2 1
8050.2.a.s yes 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8050))\):

\( T_{3} - 1 \)
\( T_{11} + 5 \)
\( T_{13} - 2 \)
\( T_{17} + 5 \)

Hecke characteristic polynomials

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