Properties

Label 2736.2.a.i
Level $2736$
Weight $2$
Character orbit 2736.a
Self dual yes
Analytic conductor $21.847$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 456)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + 3q^{7} + O(q^{10}) \) \( q - q^{5} + 3q^{7} - 5q^{11} - 2q^{13} + q^{17} - q^{19} + 4q^{23} - 4q^{25} + 6q^{29} + 10q^{31} - 3q^{35} + 11q^{43} + 9q^{47} + 2q^{49} - 10q^{53} + 5q^{55} + 4q^{59} - 5q^{61} + 2q^{65} + 4q^{67} + 8q^{71} + 13q^{73} - 15q^{77} - 4q^{79} - 4q^{83} - q^{85} + 6q^{89} - 6q^{91} + q^{95} + 2q^{97} + O(q^{100}) \)

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 0 0 −1.00000 0 3.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(19\) \(1\)

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 2736.2.a.i 1
3.b odd 2 1 912.2.a.i 1
4.b odd 2 1 1368.2.a.d 1
12.b even 2 1 456.2.a.a 1
24.f even 2 1 3648.2.a.z 1
24.h odd 2 1 3648.2.a.g 1
228.b odd 2 1 8664.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
456.2.a.a 1 12.b even 2 1
912.2.a.i 1 3.b odd 2 1
1368.2.a.d 1 4.b odd 2 1
2736.2.a.i 1 1.a even 1 1 trivial
3648.2.a.g 1 24.h odd 2 1
3648.2.a.z 1 24.f even 2 1
8664.2.a.l 1 228.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\):

\( T_{5} + 1 \)
\( T_{7} - 3 \)
\( T_{11} + 5 \)
\( T_{13} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( -3 + T \)
$11$ \( 5 + T \)
$13$ \( 2 + T \)
$17$ \( -1 + T \)
$19$ \( 1 + T \)
$23$ \( -4 + T \)
$29$ \( -6 + T \)
$31$ \( -10 + T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( -11 + T \)
$47$ \( -9 + T \)
$53$ \( 10 + T \)
$59$ \( -4 + T \)
$61$ \( 5 + T \)
$67$ \( -4 + T \)
$71$ \( -8 + T \)
$73$ \( -13 + T \)
$79$ \( 4 + T \)
$83$ \( 4 + T \)
$89$ \( -6 + T \)
$97$ \( -2 + T \)
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