Properties

Label 6080.2.a.p
Level $6080$
Weight $2$
Character orbit 6080.a
Self dual yes
Analytic conductor $48.549$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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
0 1.00000 0 −1.00000 0 1.00000 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.p 1
4.b odd 2 1 6080.2.a.h 1
8.b even 2 1 1520.2.a.d 1
8.d odd 2 1 190.2.a.c 1
24.f even 2 1 1710.2.a.d 1
40.e odd 2 1 950.2.a.a 1
40.f even 2 1 7600.2.a.m 1
40.k even 4 2 950.2.b.e 2
56.e even 2 1 9310.2.a.o 1
120.m even 2 1 8550.2.a.bd 1
152.b even 2 1 3610.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.c 1 8.d odd 2 1
950.2.a.a 1 40.e odd 2 1
950.2.b.e 2 40.k even 4 2
1520.2.a.d 1 8.b even 2 1
1710.2.a.d 1 24.f even 2 1
3610.2.a.b 1 152.b even 2 1
6080.2.a.h 1 4.b odd 2 1
6080.2.a.p 1 1.a even 1 1 trivial
7600.2.a.m 1 40.f even 2 1
8550.2.a.bd 1 120.m even 2 1
9310.2.a.o 1 56.e even 2 1

Hecke kernels

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

\( T_{3} - 1 \)
\( T_{7} - 1 \)
\( T_{11} \)

Hecke characteristic polynomials

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