Properties

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

Related objects

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 2q^{11} + q^{12} + q^{13} + q^{16} - 2q^{17} + q^{18} + 8q^{19} + 2q^{22} + q^{24} - 5q^{25} + q^{26} + q^{27} - 2q^{29} + 10q^{31} + q^{32} + 2q^{33} - 2q^{34} + q^{36} + 8q^{38} + q^{39} + 2q^{41} - 4q^{43} + 2q^{44} + 6q^{47} + q^{48} - 7q^{49} - 5q^{50} - 2q^{51} + q^{52} - 6q^{53} + q^{54} + 8q^{57} - 2q^{58} + 12q^{59} + 2q^{61} + 10q^{62} + q^{64} + 2q^{66} - 10q^{67} - 2q^{68} + 6q^{71} + q^{72} - 5q^{75} + 8q^{76} + q^{78} + q^{81} + 2q^{82} - 4q^{86} - 2q^{87} + 2q^{88} + 8q^{89} + 10q^{93} + 6q^{94} + q^{96} + 2q^{97} - 7q^{98} + 2q^{99} + O(q^{100}) \)

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 0 1.00000 0 1.00000 1.00000 0
\(n\): 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.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8034.2.a.i 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8034))\):

\( T_{5} \)
\( T_{7} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( -2 + T \)
$13$ \( -1 + T \)
$17$ \( 2 + T \)
$19$ \( -8 + T \)
$23$ \( T \)
$29$ \( 2 + T \)
$31$ \( -10 + T \)
$37$ \( T \)
$41$ \( -2 + T \)
$43$ \( 4 + T \)
$47$ \( -6 + T \)
$53$ \( 6 + T \)
$59$ \( -12 + T \)
$61$ \( -2 + T \)
$67$ \( 10 + T \)
$71$ \( -6 + T \)
$73$ \( T \)
$79$ \( T \)
$83$ \( T \)
$89$ \( -8 + T \)
$97$ \( -2 + T \)
show more
show less