Properties

Label 832.4.a.a
Level $832$
Weight $4$
Character orbit 832.a
Self dual yes
Analytic conductor $49.090$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.0895891248\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 7 q^{3} + 7 q^{5} + 13 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 7 q^{3} + 7 q^{5} + 13 q^{7} + 22 q^{9} - 26 q^{11} - 13 q^{13} - 49 q^{15} + 77 q^{17} - 126 q^{19} - 91 q^{21} + 96 q^{23} - 76 q^{25} + 35 q^{27} + 82 q^{29} - 196 q^{31} + 182 q^{33} + 91 q^{35} + 131 q^{37} + 91 q^{39} + 336 q^{41} - 201 q^{43} + 154 q^{45} + 105 q^{47} - 174 q^{49} - 539 q^{51} + 432 q^{53} - 182 q^{55} + 882 q^{57} - 294 q^{59} + 56 q^{61} + 286 q^{63} - 91 q^{65} + 478 q^{67} - 672 q^{69} - 9 q^{71} + 98 q^{73} + 532 q^{75} - 338 q^{77} - 1304 q^{79} - 839 q^{81} - 308 q^{83} + 539 q^{85} - 574 q^{87} - 1190 q^{89} - 169 q^{91} + 1372 q^{93} - 882 q^{95} + 70 q^{97} - 572 q^{99}+O(q^{100}) \) 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 −7.00000 0 7.00000 0 13.0000 0 22.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(13\) \(1\)

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 832.4.a.a 1
4.b odd 2 1 832.4.a.r 1
8.b even 2 1 208.4.a.g 1
8.d odd 2 1 13.4.a.a 1
24.f even 2 1 117.4.a.b 1
24.h odd 2 1 1872.4.a.k 1
40.e odd 2 1 325.4.a.d 1
40.k even 4 2 325.4.b.b 2
56.e even 2 1 637.4.a.a 1
88.g even 2 1 1573.4.a.a 1
104.h odd 2 1 169.4.a.e 1
104.m even 4 2 169.4.b.a 2
104.n odd 6 2 169.4.c.e 2
104.p odd 6 2 169.4.c.a 2
104.u even 12 4 169.4.e.e 4
312.h even 2 1 1521.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
13.4.a.a 1 8.d odd 2 1
117.4.a.b 1 24.f even 2 1
169.4.a.e 1 104.h odd 2 1
169.4.b.a 2 104.m even 4 2
169.4.c.a 2 104.p odd 6 2
169.4.c.e 2 104.n odd 6 2
169.4.e.e 4 104.u even 12 4
208.4.a.g 1 8.b even 2 1
325.4.a.d 1 40.e odd 2 1
325.4.b.b 2 40.k even 4 2
637.4.a.a 1 56.e even 2 1
832.4.a.a 1 1.a even 1 1 trivial
832.4.a.r 1 4.b odd 2 1
1521.4.a.a 1 312.h even 2 1
1573.4.a.a 1 88.g even 2 1
1872.4.a.k 1 24.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(832))\):

\( T_{3} + 7 \) Copy content Toggle raw display
\( T_{5} - 7 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 7 \) Copy content Toggle raw display
$5$ \( T - 7 \) Copy content Toggle raw display
$7$ \( T - 13 \) Copy content Toggle raw display
$11$ \( T + 26 \) Copy content Toggle raw display
$13$ \( T + 13 \) Copy content Toggle raw display
$17$ \( T - 77 \) Copy content Toggle raw display
$19$ \( T + 126 \) Copy content Toggle raw display
$23$ \( T - 96 \) Copy content Toggle raw display
$29$ \( T - 82 \) Copy content Toggle raw display
$31$ \( T + 196 \) Copy content Toggle raw display
$37$ \( T - 131 \) Copy content Toggle raw display
$41$ \( T - 336 \) Copy content Toggle raw display
$43$ \( T + 201 \) Copy content Toggle raw display
$47$ \( T - 105 \) Copy content Toggle raw display
$53$ \( T - 432 \) Copy content Toggle raw display
$59$ \( T + 294 \) Copy content Toggle raw display
$61$ \( T - 56 \) Copy content Toggle raw display
$67$ \( T - 478 \) Copy content Toggle raw display
$71$ \( T + 9 \) Copy content Toggle raw display
$73$ \( T - 98 \) Copy content Toggle raw display
$79$ \( T + 1304 \) Copy content Toggle raw display
$83$ \( T + 308 \) Copy content Toggle raw display
$89$ \( T + 1190 \) Copy content Toggle raw display
$97$ \( T - 70 \) Copy content Toggle raw display
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