Properties

Label 1856.2.a.d
Level $1856$
Weight $2$
Character orbit 1856.a
Self dual yes
Analytic conductor $14.820$
Analytic rank $2$
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: \(2\)
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

\(f(q)\) \(=\) \( q - q^{3} - 3 q^{5} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( q - q^{3} - 3 q^{5} - 4 q^{7} - 2 q^{9} - 3 q^{11} - 5 q^{13} + 3 q^{15} - 6 q^{17} + 4 q^{19} + 4 q^{21} - 6 q^{23} + 4 q^{25} + 5 q^{27} + q^{29} + 5 q^{31} + 3 q^{33} + 12 q^{35} - 8 q^{37} + 5 q^{39} + q^{43} + 6 q^{45} - 3 q^{47} + 9 q^{49} + 6 q^{51} - 3 q^{53} + 9 q^{55} - 4 q^{57} - 6 q^{59} - 2 q^{61} + 8 q^{63} + 15 q^{65} - 8 q^{67} + 6 q^{69} + 6 q^{71} - 16 q^{73} - 4 q^{75} + 12 q^{77} + 11 q^{79} + q^{81} - 6 q^{83} + 18 q^{85} - q^{87} - 12 q^{89} + 20 q^{91} - 5 q^{93} - 12 q^{95} + 8 q^{97} + 6 q^{99} + O(q^{100}) \)

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 −3.00000 0 −4.00000 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.d 1
4.b odd 2 1 1856.2.a.i 1
8.b even 2 1 116.2.a.b 1
8.d odd 2 1 464.2.a.c 1
24.f even 2 1 4176.2.a.f 1
24.h odd 2 1 1044.2.a.b 1
40.f even 2 1 2900.2.a.b 1
40.i odd 4 2 2900.2.c.c 2
56.h odd 2 1 5684.2.a.d 1
232.g even 2 1 3364.2.a.b 1
232.l odd 4 2 3364.2.c.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
116.2.a.b 1 8.b even 2 1
464.2.a.c 1 8.d odd 2 1
1044.2.a.b 1 24.h odd 2 1
1856.2.a.d 1 1.a even 1 1 trivial
1856.2.a.i 1 4.b odd 2 1
2900.2.a.b 1 40.f even 2 1
2900.2.c.c 2 40.i odd 4 2
3364.2.a.b 1 232.g even 2 1
3364.2.c.a 2 232.l odd 4 2
4176.2.a.f 1 24.f even 2 1
5684.2.a.d 1 56.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} + 1 \)
\( T_{5} + 3 \)
\( T_{17} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( 3 + T \)
$7$ \( 4 + T \)
$11$ \( 3 + T \)
$13$ \( 5 + T \)
$17$ \( 6 + T \)
$19$ \( -4 + T \)
$23$ \( 6 + T \)
$29$ \( -1 + T \)
$31$ \( -5 + T \)
$37$ \( 8 + T \)
$41$ \( T \)
$43$ \( -1 + T \)
$47$ \( 3 + T \)
$53$ \( 3 + T \)
$59$ \( 6 + T \)
$61$ \( 2 + T \)
$67$ \( 8 + T \)
$71$ \( -6 + T \)
$73$ \( 16 + T \)
$79$ \( -11 + T \)
$83$ \( 6 + T \)
$89$ \( 12 + T \)
$97$ \( -8 + T \)
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