Properties

Label 1856.2.a.f
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 58)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} - q^{5} + 2 q^{7} - 2 q^{9} - 3 q^{11} + q^{13} + q^{15} + 8 q^{17} - 2 q^{21} - 4 q^{23} - 4 q^{25} + 5 q^{27} + q^{29} + 3 q^{31} + 3 q^{33} - 2 q^{35} - 8 q^{37} - q^{39} + 2 q^{41} - 11 q^{43} + 2 q^{45} - 13 q^{47} - 3 q^{49} - 8 q^{51} + 11 q^{53} + 3 q^{55} + 8 q^{61} - 4 q^{63} - q^{65} - 12 q^{67} + 4 q^{69} - 2 q^{71} + 4 q^{73} + 4 q^{75} - 6 q^{77} - 15 q^{79} + q^{81} + 4 q^{83} - 8 q^{85} - q^{87} - 10 q^{89} + 2 q^{91} - 3 q^{93} - 2 q^{97} + 6 q^{99}+O(q^{100}) \) 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 2.00000 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.f 1
4.b odd 2 1 1856.2.a.k 1
8.b even 2 1 464.2.a.e 1
8.d odd 2 1 58.2.a.b 1
24.f even 2 1 522.2.a.b 1
24.h odd 2 1 4176.2.a.n 1
40.e odd 2 1 1450.2.a.c 1
40.k even 4 2 1450.2.b.b 2
56.e even 2 1 2842.2.a.e 1
88.g even 2 1 7018.2.a.a 1
104.h odd 2 1 9802.2.a.a 1
232.b odd 2 1 1682.2.a.d 1
232.k even 4 2 1682.2.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.2.a.b 1 8.d odd 2 1
464.2.a.e 1 8.b even 2 1
522.2.a.b 1 24.f even 2 1
1450.2.a.c 1 40.e odd 2 1
1450.2.b.b 2 40.k even 4 2
1682.2.a.d 1 232.b odd 2 1
1682.2.b.a 2 232.k even 4 2
1856.2.a.f 1 1.a even 1 1 trivial
1856.2.a.k 1 4.b odd 2 1
2842.2.a.e 1 56.e even 2 1
4176.2.a.n 1 24.h odd 2 1
7018.2.a.a 1 88.g even 2 1
9802.2.a.a 1 104.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{5} + 1 \) Copy content Toggle raw display
\( T_{17} - 8 \) 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
$7$ \( T - 2 \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T - 8 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T - 1 \) Copy content Toggle raw display
$31$ \( T - 3 \) Copy content Toggle raw display
$37$ \( T + 8 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T + 11 \) Copy content Toggle raw display
$47$ \( T + 13 \) Copy content Toggle raw display
$53$ \( T - 11 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 8 \) Copy content Toggle raw display
$67$ \( T + 12 \) Copy content Toggle raw display
$71$ \( T + 2 \) Copy content Toggle raw display
$73$ \( T - 4 \) Copy content Toggle raw display
$79$ \( T + 15 \) Copy content Toggle raw display
$83$ \( T - 4 \) Copy content Toggle raw display
$89$ \( T + 10 \) Copy content Toggle raw display
$97$ \( T + 2 \) Copy content Toggle raw display
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