Properties

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

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(109.507544971\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 58)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 7 q^{3} - 5 q^{5} - 2 q^{7} + 22 q^{9} + O(q^{10}) \) \( q - 7 q^{3} - 5 q^{5} - 2 q^{7} + 22 q^{9} - 37 q^{11} - 27 q^{13} + 35 q^{15} + 24 q^{17} + 88 q^{19} + 14 q^{21} - 28 q^{23} - 100 q^{25} + 35 q^{27} + 29 q^{29} - 143 q^{31} + 259 q^{33} + 10 q^{35} + 360 q^{37} + 189 q^{39} + 386 q^{41} - 381 q^{43} - 110 q^{45} - 103 q^{47} - 339 q^{49} - 168 q^{51} + 431 q^{53} + 185 q^{55} - 616 q^{57} - 288 q^{59} + 840 q^{61} - 44 q^{63} + 135 q^{65} + 180 q^{67} + 196 q^{69} + 706 q^{71} + 716 q^{73} + 700 q^{75} + 74 q^{77} + 931 q^{79} - 839 q^{81} - 1188 q^{83} - 120 q^{85} - 203 q^{87} - 642 q^{89} + 54 q^{91} + 1001 q^{93} - 440 q^{95} + 486 q^{97} - 814 q^{99} + O(q^{100}) \)

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 −5.00000 0 −2.00000 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.a 1
4.b odd 2 1 1856.4.a.d 1
8.b even 2 1 58.4.a.a 1
8.d odd 2 1 464.4.a.a 1
24.h odd 2 1 522.4.a.e 1
40.f even 2 1 1450.4.a.e 1
232.g even 2 1 1682.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.4.a.a 1 8.b even 2 1
464.4.a.a 1 8.d odd 2 1
522.4.a.e 1 24.h odd 2 1
1450.4.a.e 1 40.f even 2 1
1682.4.a.b 1 232.g even 2 1
1856.4.a.a 1 1.a even 1 1 trivial
1856.4.a.d 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} + 7 \)
\( T_{5} + 5 \)
\( T_{7} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 7 + T \)
$5$ \( 5 + T \)
$7$ \( 2 + T \)
$11$ \( 37 + T \)
$13$ \( 27 + T \)
$17$ \( -24 + T \)
$19$ \( -88 + T \)
$23$ \( 28 + T \)
$29$ \( -29 + T \)
$31$ \( 143 + T \)
$37$ \( -360 + T \)
$41$ \( -386 + T \)
$43$ \( 381 + T \)
$47$ \( 103 + T \)
$53$ \( -431 + T \)
$59$ \( 288 + T \)
$61$ \( -840 + T \)
$67$ \( -180 + T \)
$71$ \( -706 + T \)
$73$ \( -716 + T \)
$79$ \( -931 + T \)
$83$ \( 1188 + T \)
$89$ \( 642 + T \)
$97$ \( -486 + T \)
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