Properties

Label 5684.2.a.k
Level $5684$
Weight $2$
Character orbit 5684.a
Self dual yes
Analytic conductor $45.387$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5684 = 2^{2} \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5684.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.3869685089\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 116)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{3} - 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 3 q^{3} - 3 q^{5} + 6 q^{9} - q^{11} + 3 q^{13} - 9 q^{15} - 2 q^{17} - 4 q^{19} - 6 q^{23} + 4 q^{25} + 9 q^{27} - q^{29} - 9 q^{31} - 3 q^{33} - 8 q^{37} + 9 q^{39} + 8 q^{41} - 5 q^{43} - 18 q^{45} + 7 q^{47} - 6 q^{51} - 5 q^{53} + 3 q^{55} - 12 q^{57} + 10 q^{59} - 10 q^{61} - 9 q^{65} + 8 q^{67} - 18 q^{69} - 2 q^{71} + 12 q^{75} - q^{79} + 9 q^{81} - 6 q^{83} + 6 q^{85} - 3 q^{87} - 12 q^{89} - 27 q^{93} + 12 q^{95} - 6 q^{99}+O(q^{100}) \) 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 −3.00000 0 0 0 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(-1\)
\(29\) \(1\)

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 5684.2.a.k 1
7.b odd 2 1 116.2.a.a 1
21.c even 2 1 1044.2.a.c 1
28.d even 2 1 464.2.a.g 1
35.c odd 2 1 2900.2.a.e 1
35.f even 4 2 2900.2.c.a 2
56.e even 2 1 1856.2.a.a 1
56.h odd 2 1 1856.2.a.o 1
84.h odd 2 1 4176.2.a.c 1
203.c odd 2 1 3364.2.a.c 1
203.g even 4 2 3364.2.c.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
116.2.a.a 1 7.b odd 2 1
464.2.a.g 1 28.d even 2 1
1044.2.a.c 1 21.c even 2 1
1856.2.a.a 1 56.e even 2 1
1856.2.a.o 1 56.h odd 2 1
2900.2.a.e 1 35.c odd 2 1
2900.2.c.a 2 35.f even 4 2
3364.2.a.c 1 203.c odd 2 1
3364.2.c.b 2 203.g even 4 2
4176.2.a.c 1 84.h odd 2 1
5684.2.a.k 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5684))\):

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