Properties

Label 5796.2.a.l
Level $5796$
Weight $2$
Character orbit 5796.a
Self dual yes
Analytic conductor $46.281$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.2812930115\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1932)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{5})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta q^{5} - q^{7} + 3 q^{11} + (\beta - 1) q^{13} + ( - 6 \beta + 3) q^{17} + ( - 2 \beta - 1) q^{19} + q^{23} + (\beta - 4) q^{25} + ( - 2 \beta + 5) q^{29} - 3 q^{31} - \beta q^{35} + (4 \beta + 3) q^{37} + (8 \beta - 1) q^{41} + ( - 5 \beta - 1) q^{43} + (2 \beta + 6) q^{47} + q^{49} + (7 \beta - 2) q^{53} + 3 \beta q^{55} + (\beta + 8) q^{59} + (3 \beta + 1) q^{61} + q^{65} + (9 \beta - 8) q^{67} + (\beta + 3) q^{71} + ( - 2 \beta + 5) q^{73} - 3 q^{77} + ( - 6 \beta + 3) q^{79} + (4 \beta + 1) q^{83} + ( - 3 \beta - 6) q^{85} + (11 \beta - 1) q^{89} + ( - \beta + 1) q^{91} + ( - 3 \beta - 2) q^{95} + ( - 12 \beta + 7) q^{97} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{5} - 2 q^{7} + 6 q^{11} - q^{13} - 4 q^{19} + 2 q^{23} - 7 q^{25} + 8 q^{29} - 6 q^{31} - q^{35} + 10 q^{37} + 6 q^{41} - 7 q^{43} + 14 q^{47} + 2 q^{49} + 3 q^{53} + 3 q^{55} + 17 q^{59} + 5 q^{61} + 2 q^{65} - 7 q^{67} + 7 q^{71} + 8 q^{73} - 6 q^{77} + 6 q^{83} - 15 q^{85} + 9 q^{89} + q^{91} - 7 q^{95} + 2 q^{97}+O(q^{100}) \) 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
−0.618034
1.61803
0 0 0 −0.618034 0 −1.00000 0 0 0
1.2 0 0 0 1.61803 0 −1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(1\)
\(23\) \(-1\)

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 5796.2.a.l 2
3.b odd 2 1 1932.2.a.g 2
12.b even 2 1 7728.2.a.ba 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.2.a.g 2 3.b odd 2 1
5796.2.a.l 2 1.a even 1 1 trivial
7728.2.a.ba 2 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5796))\):

\( T_{5}^{2} - T_{5} - 1 \) Copy content Toggle raw display
\( T_{11} - 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{2} \) Copy content Toggle raw display
$3$ \( T^{2} \) Copy content Toggle raw display
$5$ \( T^{2} - T - 1 \) Copy content Toggle raw display
$7$ \( (T + 1)^{2} \) Copy content Toggle raw display
$11$ \( (T - 3)^{2} \) Copy content Toggle raw display
$13$ \( T^{2} + T - 1 \) Copy content Toggle raw display
$17$ \( T^{2} - 45 \) Copy content Toggle raw display
$19$ \( T^{2} + 4T - 1 \) Copy content Toggle raw display
$23$ \( (T - 1)^{2} \) Copy content Toggle raw display
$29$ \( T^{2} - 8T + 11 \) Copy content Toggle raw display
$31$ \( (T + 3)^{2} \) Copy content Toggle raw display
$37$ \( T^{2} - 10T + 5 \) Copy content Toggle raw display
$41$ \( T^{2} - 6T - 71 \) Copy content Toggle raw display
$43$ \( T^{2} + 7T - 19 \) Copy content Toggle raw display
$47$ \( T^{2} - 14T + 44 \) Copy content Toggle raw display
$53$ \( T^{2} - 3T - 59 \) Copy content Toggle raw display
$59$ \( T^{2} - 17T + 71 \) Copy content Toggle raw display
$61$ \( T^{2} - 5T - 5 \) Copy content Toggle raw display
$67$ \( T^{2} + 7T - 89 \) Copy content Toggle raw display
$71$ \( T^{2} - 7T + 11 \) Copy content Toggle raw display
$73$ \( T^{2} - 8T + 11 \) Copy content Toggle raw display
$79$ \( T^{2} - 45 \) Copy content Toggle raw display
$83$ \( T^{2} - 6T - 11 \) Copy content Toggle raw display
$89$ \( T^{2} - 9T - 131 \) Copy content Toggle raw display
$97$ \( T^{2} - 2T - 179 \) Copy content Toggle raw display
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