Properties

Label 1792.2.a.d
Level $1792$
Weight $2$
Character orbit 1792.a
Self dual yes
Analytic conductor $14.309$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 448)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{3} + 4q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{3} + 4q^{5} - q^{7} + q^{9} - 2q^{11} - 4q^{13} - 8q^{15} + 2q^{17} + 6q^{19} + 2q^{21} + 11q^{25} + 4q^{27} + 8q^{29} - 8q^{31} + 4q^{33} - 4q^{35} + 8q^{37} + 8q^{39} - 10q^{41} - 2q^{43} + 4q^{45} + 8q^{47} + q^{49} - 4q^{51} - 8q^{55} - 12q^{57} + 10q^{59} + 4q^{61} - q^{63} - 16q^{65} + 2q^{67} - 8q^{71} + 6q^{73} - 22q^{75} + 2q^{77} + 8q^{79} - 11q^{81} + 6q^{83} + 8q^{85} - 16q^{87} - 10q^{89} + 4q^{91} + 16q^{93} + 24q^{95} + 2q^{97} - 2q^{99} + O(q^{100}) \)

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 −2.00000 0 4.00000 0 −1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(1\)

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 1792.2.a.d 1
4.b odd 2 1 1792.2.a.h 1
8.b even 2 1 1792.2.a.e 1
8.d odd 2 1 1792.2.a.a 1
16.e even 4 2 448.2.b.b yes 2
16.f odd 4 2 448.2.b.a 2
48.i odd 4 2 4032.2.c.f 2
48.k even 4 2 4032.2.c.b 2
112.j even 4 2 3136.2.b.c 2
112.l odd 4 2 3136.2.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
448.2.b.a 2 16.f odd 4 2
448.2.b.b yes 2 16.e even 4 2
1792.2.a.a 1 8.d odd 2 1
1792.2.a.d 1 1.a even 1 1 trivial
1792.2.a.e 1 8.b even 2 1
1792.2.a.h 1 4.b odd 2 1
3136.2.b.a 2 112.l odd 4 2
3136.2.b.c 2 112.j even 4 2
4032.2.c.b 2 48.k even 4 2
4032.2.c.f 2 48.i odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1792))\):

\( T_{3} + 2 \)
\( T_{5} - 4 \)
\( T_{23} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 2 + T \)
$5$ \( -4 + T \)
$7$ \( 1 + T \)
$11$ \( 2 + T \)
$13$ \( 4 + T \)
$17$ \( -2 + T \)
$19$ \( -6 + T \)
$23$ \( T \)
$29$ \( -8 + T \)
$31$ \( 8 + T \)
$37$ \( -8 + T \)
$41$ \( 10 + T \)
$43$ \( 2 + T \)
$47$ \( -8 + T \)
$53$ \( T \)
$59$ \( -10 + T \)
$61$ \( -4 + T \)
$67$ \( -2 + T \)
$71$ \( 8 + T \)
$73$ \( -6 + T \)
$79$ \( -8 + T \)
$83$ \( -6 + T \)
$89$ \( 10 + T \)
$97$ \( -2 + T \)
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