Properties

Label 1856.4.a.b
Level $1856$
Weight $4$
Character orbit 1856.a
Self dual yes
Analytic conductor $109.508$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.507544971\)
Analytic rank: \(2\)
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

\(f(q)\) \(=\) \( q - 7 q^{3} + 13 q^{5} - 16 q^{7} + 22 q^{9} + O(q^{10}) \) \( q - 7 q^{3} + 13 q^{5} - 16 q^{7} + 22 q^{9} - 45 q^{11} - 61 q^{13} - 91 q^{15} - 102 q^{17} - 68 q^{19} + 112 q^{21} - 194 q^{23} + 44 q^{25} + 35 q^{27} + 29 q^{29} - 149 q^{31} + 315 q^{33} - 208 q^{35} - 400 q^{37} + 427 q^{39} + 280 q^{41} + 263 q^{43} + 286 q^{45} - 509 q^{47} - 87 q^{49} + 714 q^{51} + 605 q^{53} - 585 q^{55} + 476 q^{57} - 578 q^{59} + 718 q^{61} - 352 q^{63} - 793 q^{65} - 260 q^{67} + 1358 q^{69} - 738 q^{71} + 652 q^{73} - 308 q^{75} + 720 q^{77} + 917 q^{79} - 839 q^{81} + 678 q^{83} - 1326 q^{85} - 203 q^{87} - 1008 q^{89} + 976 q^{91} + 1043 q^{93} - 884 q^{95} - 1764 q^{97} - 990 q^{99} + O(q^{100}) \)

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 −7.00000 0 13.0000 0 −16.0000 0 22.0000 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 1856.4.a.b 1
4.b odd 2 1 1856.4.a.e 1
8.b even 2 1 928.4.a.b yes 1
8.d odd 2 1 928.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
928.4.a.a 1 8.d odd 2 1
928.4.a.b yes 1 8.b even 2 1
1856.4.a.b 1 1.a even 1 1 trivial
1856.4.a.e 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} + 7 \)
\( T_{5} - 13 \)
\( T_{7} + 16 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 7 + T \)
$5$ \( -13 + T \)
$7$ \( 16 + T \)
$11$ \( 45 + T \)
$13$ \( 61 + T \)
$17$ \( 102 + T \)
$19$ \( 68 + T \)
$23$ \( 194 + T \)
$29$ \( -29 + T \)
$31$ \( 149 + T \)
$37$ \( 400 + T \)
$41$ \( -280 + T \)
$43$ \( -263 + T \)
$47$ \( 509 + T \)
$53$ \( -605 + T \)
$59$ \( 578 + T \)
$61$ \( -718 + T \)
$67$ \( 260 + T \)
$71$ \( 738 + T \)
$73$ \( -652 + T \)
$79$ \( -917 + T \)
$83$ \( -678 + T \)
$89$ \( 1008 + T \)
$97$ \( 1764 + T \)
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