Properties

Label 1856.4.a.c
Level $1856$
Weight $4$
Character orbit 1856.a
Self dual yes
Analytic conductor $109.508$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - 7 q^{3} + 15 q^{5} + 18 q^{7} + 22 q^{9} + O(q^{10}) \) \( q - 7 q^{3} + 15 q^{5} + 18 q^{7} + 22 q^{9} + 27 q^{11} + 57 q^{13} - 105 q^{15} - 44 q^{17} + 152 q^{19} - 126 q^{21} + 152 q^{23} + 100 q^{25} + 35 q^{27} + 29 q^{29} + 173 q^{31} - 189 q^{33} + 270 q^{35} + 120 q^{37} - 399 q^{39} - 314 q^{41} + 339 q^{43} + 330 q^{45} + 357 q^{47} - 19 q^{49} + 308 q^{51} + 59 q^{53} + 405 q^{55} - 1064 q^{57} - 572 q^{59} + 420 q^{61} + 396 q^{63} + 855 q^{65} + 660 q^{67} - 1064 q^{69} - 726 q^{71} + 1004 q^{73} - 700 q^{75} + 486 q^{77} - 361 q^{79} - 839 q^{81} - 168 q^{83} - 660 q^{85} - 203 q^{87} + 58 q^{89} + 1026 q^{91} - 1211 q^{93} + 2280 q^{95} - 1206 q^{97} + 594 q^{99} + O(q^{100}) \)

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 15.0000 0 18.0000 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.c 1
4.b odd 2 1 1856.4.a.f 1
8.b even 2 1 464.4.a.b 1
8.d odd 2 1 58.4.a.b 1
24.f even 2 1 522.4.a.b 1
40.e odd 2 1 1450.4.a.d 1
232.b odd 2 1 1682.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.4.a.b 1 8.d odd 2 1
464.4.a.b 1 8.b even 2 1
522.4.a.b 1 24.f even 2 1
1450.4.a.d 1 40.e odd 2 1
1682.4.a.a 1 232.b odd 2 1
1856.4.a.c 1 1.a even 1 1 trivial
1856.4.a.f 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} + 7 \)
\( T_{5} - 15 \)
\( T_{7} - 18 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 7 + T \)
$5$ \( -15 + T \)
$7$ \( -18 + T \)
$11$ \( -27 + T \)
$13$ \( -57 + T \)
$17$ \( 44 + T \)
$19$ \( -152 + T \)
$23$ \( -152 + T \)
$29$ \( -29 + T \)
$31$ \( -173 + T \)
$37$ \( -120 + T \)
$41$ \( 314 + T \)
$43$ \( -339 + T \)
$47$ \( -357 + T \)
$53$ \( -59 + T \)
$59$ \( 572 + T \)
$61$ \( -420 + T \)
$67$ \( -660 + T \)
$71$ \( 726 + T \)
$73$ \( -1004 + T \)
$79$ \( 361 + T \)
$83$ \( 168 + T \)
$89$ \( -58 + T \)
$97$ \( 1206 + T \)
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