Properties

Label 8281.2.a.j
Level $8281$
Weight $2$
Character orbit 8281.a
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 6 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 9 q^{15} - q^{16} + 2 q^{17} + 6 q^{18} + q^{19} + 3 q^{20} - 3 q^{22} - 9 q^{24} + 4 q^{25} + 9 q^{27} + 7 q^{29} - 9 q^{30} - 3 q^{31} + 5 q^{32} - 9 q^{33} + 2 q^{34} - 6 q^{36} + 2 q^{37} + q^{38} + 9 q^{40} - 3 q^{41} - 7 q^{43} + 3 q^{44} - 18 q^{45} - q^{47} - 3 q^{48} + 4 q^{50} + 6 q^{51} + 3 q^{53} + 9 q^{54} + 9 q^{55} + 3 q^{57} + 7 q^{58} + 4 q^{59} + 9 q^{60} + 13 q^{61} - 3 q^{62} + 7 q^{64} - 9 q^{66} - 3 q^{67} - 2 q^{68} + 13 q^{71} - 18 q^{72} + 13 q^{73} + 2 q^{74} + 12 q^{75} - q^{76} - 3 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{85} - 7 q^{86} + 21 q^{87} + 9 q^{88} - 6 q^{89} - 18 q^{90} - 9 q^{93} - q^{94} - 3 q^{95} + 15 q^{96} + 5 q^{97} - 18 q^{99}+O(q^{100}) \) 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
1.00000 3.00000 −1.00000 −3.00000 3.00000 0 −3.00000 6.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(13\) \(1\)

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 8281.2.a.j 1
7.b odd 2 1 8281.2.a.i 1
7.d odd 6 2 1183.2.e.a 2
13.b even 2 1 8281.2.a.g 1
13.c even 3 2 637.2.f.a 2
91.b odd 2 1 8281.2.a.c 1
91.g even 3 2 637.2.g.a 2
91.h even 3 2 637.2.h.a 2
91.m odd 6 2 91.2.g.a 2
91.n odd 6 2 637.2.f.b 2
91.s odd 6 2 1183.2.e.c 2
91.v odd 6 2 91.2.h.a yes 2
273.r even 6 2 819.2.s.a 2
273.bf even 6 2 819.2.n.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.g.a 2 91.m odd 6 2
91.2.h.a yes 2 91.v odd 6 2
637.2.f.a 2 13.c even 3 2
637.2.f.b 2 91.n odd 6 2
637.2.g.a 2 91.g even 3 2
637.2.h.a 2 91.h even 3 2
819.2.n.c 2 273.bf even 6 2
819.2.s.a 2 273.r even 6 2
1183.2.e.a 2 7.d odd 6 2
1183.2.e.c 2 91.s odd 6 2
8281.2.a.c 1 91.b odd 2 1
8281.2.a.g 1 13.b even 2 1
8281.2.a.i 1 7.b odd 2 1
8281.2.a.j 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8281))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{3} - 3 \) Copy content Toggle raw display
\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{11} + 3 \) Copy content Toggle raw display
\( T_{17} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

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