Properties

Label 8034.2.a.c
Level $8034$
Weight $2$
Character orbit 8034.a
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} - q^{13} - 3q^{14} + q^{15} + q^{16} - q^{18} + 4q^{19} + q^{20} + 3q^{21} - 2q^{22} - q^{24} - 4q^{25} + q^{26} + q^{27} + 3q^{28} + 7q^{29} - q^{30} - 4q^{31} - q^{32} + 2q^{33} + 3q^{35} + q^{36} + 2q^{37} - 4q^{38} - q^{39} - q^{40} - 6q^{41} - 3q^{42} + 2q^{43} + 2q^{44} + q^{45} + 13q^{47} + q^{48} + 2q^{49} + 4q^{50} - q^{52} + 2q^{53} - q^{54} + 2q^{55} - 3q^{56} + 4q^{57} - 7q^{58} - 5q^{59} + q^{60} + 4q^{61} + 4q^{62} + 3q^{63} + q^{64} - q^{65} - 2q^{66} - q^{67} - 3q^{70} - q^{72} + 3q^{73} - 2q^{74} - 4q^{75} + 4q^{76} + 6q^{77} + q^{78} - 4q^{79} + q^{80} + q^{81} + 6q^{82} - q^{83} + 3q^{84} - 2q^{86} + 7q^{87} - 2q^{88} - 8q^{89} - q^{90} - 3q^{91} - 4q^{93} - 13q^{94} + 4q^{95} - q^{96} + 14q^{97} - 2q^{98} + 2q^{99} + O(q^{100}) \)

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 1.00000 −1.00000 3.00000 −1.00000 1.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(13\) \(1\)
\(103\) \(1\)

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 8034.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8034.2.a.c 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8034))\):

\( T_{5} - 1 \)
\( T_{7} - 3 \)

Hecke characteristic polynomials

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