Properties

Label 1856.2.a.l
Level $1856$
Weight $2$
Character orbit 1856.a
Self dual yes
Analytic conductor $14.820$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8202346151\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 928)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} + q^{5} - 2 q^{9} - 5 q^{11} - q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + 6 q^{23} - 4 q^{25} - 5 q^{27} + q^{29} - 9 q^{31} - 5 q^{33} - q^{39} - 8 q^{41} - q^{43} - 2 q^{45} - 9 q^{47} - 7 q^{49} - 6 q^{51} + 9 q^{53} - 5 q^{55} + 4 q^{57} + 14 q^{59} - 10 q^{61} - q^{65} - 4 q^{67} + 6 q^{69} + 6 q^{71} - 4 q^{73} - 4 q^{75} + 17 q^{79} + q^{81} + 6 q^{83} - 6 q^{85} + q^{87} - 9 q^{93} + 4 q^{95} - 4 q^{97} + 10 q^{99}+O(q^{100}) \) 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 1.00000 0 1.00000 0 0 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 1856.2.a.l 1
4.b odd 2 1 1856.2.a.g 1
8.b even 2 1 928.2.a.a 1
8.d odd 2 1 928.2.a.b yes 1
24.f even 2 1 8352.2.a.h 1
24.h odd 2 1 8352.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
928.2.a.a 1 8.b even 2 1
928.2.a.b yes 1 8.d odd 2 1
1856.2.a.g 1 4.b odd 2 1
1856.2.a.l 1 1.a even 1 1 trivial
8352.2.a.g 1 24.h odd 2 1
8352.2.a.h 1 24.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{5} - 1 \) Copy content Toggle raw display
\( T_{17} + 6 \) 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
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 5 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T + 6 \) 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
$37$ \( T \) Copy content Toggle raw display
$41$ \( T + 8 \) Copy content Toggle raw display
$43$ \( T + 1 \) Copy content Toggle raw display
$47$ \( T + 9 \) Copy content Toggle raw display
$53$ \( T - 9 \) Copy content Toggle raw display
$59$ \( T - 14 \) Copy content Toggle raw display
$61$ \( T + 10 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T - 6 \) Copy content Toggle raw display
$73$ \( T + 4 \) Copy content Toggle raw display
$79$ \( T - 17 \) Copy content Toggle raw display
$83$ \( T - 6 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T + 4 \) Copy content Toggle raw display
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