Properties

Label 6080.2.a.g
Level $6080$
Weight $2$
Character orbit 6080.a
Self dual yes
Analytic conductor $48.549$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6080.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.5490444289\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3040)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} - q^{5} - 3 q^{7} - 2 q^{9} - 5 q^{13} + q^{15} - 3 q^{17} - q^{19} + 3 q^{21} - 7 q^{23} + q^{25} + 5 q^{27} + q^{29} - 2 q^{31} + 3 q^{35} - 2 q^{37} + 5 q^{39} - 10 q^{41} - 6 q^{43} + 2 q^{45} - 8 q^{47} + 2 q^{49} + 3 q^{51} - 9 q^{53} + q^{57} + 5 q^{59} - 4 q^{61} + 6 q^{63} + 5 q^{65} - q^{67} + 7 q^{69} - 12 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} + q^{81} + 18 q^{83} + 3 q^{85} - q^{87} + 2 q^{89} + 15 q^{91} + 2 q^{93} + q^{95} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
0 −1.00000 0 −1.00000 0 −3.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(19\) \(1\)

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 6080.2.a.g 1
4.b odd 2 1 6080.2.a.q 1
8.b even 2 1 3040.2.a.d yes 1
8.d odd 2 1 3040.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3040.2.a.a 1 8.d odd 2 1
3040.2.a.d yes 1 8.b even 2 1
6080.2.a.g 1 1.a even 1 1 trivial
6080.2.a.q 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6080))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{7} + 3 \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T + 5 \) Copy content Toggle raw display
$17$ \( T + 3 \) Copy content Toggle raw display
$19$ \( T + 1 \) Copy content Toggle raw display
$23$ \( T + 7 \) Copy content Toggle raw display
$29$ \( T - 1 \) Copy content Toggle raw display
$31$ \( T + 2 \) Copy content Toggle raw display
$37$ \( T + 2 \) Copy content Toggle raw display
$41$ \( T + 10 \) Copy content Toggle raw display
$43$ \( T + 6 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T + 9 \) Copy content Toggle raw display
$59$ \( T - 5 \) Copy content Toggle raw display
$61$ \( T + 4 \) Copy content Toggle raw display
$67$ \( T + 1 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T + 13 \) Copy content Toggle raw display
$79$ \( T - 6 \) Copy content Toggle raw display
$83$ \( T - 18 \) Copy content Toggle raw display
$89$ \( T - 2 \) Copy content Toggle raw display
$97$ \( T + 14 \) Copy content Toggle raw display
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