Properties

Label 6080.2.a.w
Level $6080$
Weight $2$
Character orbit 6080.a
Self dual yes
Analytic conductor $48.549$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 760)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{3} - q^{5} + q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 3 q^{3} - q^{5} + q^{7} + 6 q^{9} + 4 q^{11} - q^{13} - 3 q^{15} - 7 q^{17} - q^{19} + 3 q^{21} + 5 q^{23} + q^{25} + 9 q^{27} - 7 q^{29} + 2 q^{31} + 12 q^{33} - q^{35} + 6 q^{37} - 3 q^{39} + 6 q^{41} + 10 q^{43} - 6 q^{45} + 8 q^{47} - 6 q^{49} - 21 q^{51} + 3 q^{53} - 4 q^{55} - 3 q^{57} + 5 q^{59} + 8 q^{61} + 6 q^{63} + q^{65} + 11 q^{67} + 15 q^{69} + 12 q^{71} - 9 q^{73} + 3 q^{75} + 4 q^{77} - 6 q^{79} + 9 q^{81} + 14 q^{83} + 7 q^{85} - 21 q^{87} - 6 q^{89} - q^{91} + 6 q^{93} + q^{95} - 2 q^{97} + 24 q^{99}+O(q^{100}) \) 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 3.00000 0 −1.00000 0 1.00000 0 6.00000 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.w 1
4.b odd 2 1 6080.2.a.a 1
8.b even 2 1 1520.2.a.a 1
8.d odd 2 1 760.2.a.e 1
24.f even 2 1 6840.2.a.c 1
40.e odd 2 1 3800.2.a.a 1
40.f even 2 1 7600.2.a.t 1
40.k even 4 2 3800.2.d.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
760.2.a.e 1 8.d odd 2 1
1520.2.a.a 1 8.b even 2 1
3800.2.a.a 1 40.e odd 2 1
3800.2.d.a 2 40.k even 4 2
6080.2.a.a 1 4.b odd 2 1
6080.2.a.w 1 1.a even 1 1 trivial
6840.2.a.c 1 24.f even 2 1
7600.2.a.t 1 40.f even 2 1

Hecke kernels

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

\( T_{3} - 3 \) Copy content Toggle raw display
\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{11} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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