Properties

Label 2736.2.a.p
Level $2736$
Weight $2$
Character orbit 2736.a
Self dual yes
Analytic conductor $21.847$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{5} + 3q^{7} + O(q^{10}) \) \( q + q^{5} + 3q^{7} - 3q^{11} - 4q^{13} - 5q^{17} + q^{19} - 4q^{25} - 2q^{29} - 8q^{31} + 3q^{35} - 10q^{37} - 6q^{41} + 7q^{43} - 9q^{47} + 2q^{49} + 8q^{53} - 3q^{55} + 14q^{59} - 5q^{61} - 4q^{65} - 6q^{71} - 15q^{73} - 9q^{77} + 4q^{79} + 4q^{83} - 5q^{85} - 12q^{91} + q^{95} + 16q^{97} + O(q^{100}) \)

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.p 1
3.b odd 2 1 304.2.a.e 1
4.b odd 2 1 1368.2.a.h 1
12.b even 2 1 152.2.a.a 1
15.d odd 2 1 7600.2.a.b 1
24.f even 2 1 1216.2.a.p 1
24.h odd 2 1 1216.2.a.d 1
57.d even 2 1 5776.2.a.b 1
60.h even 2 1 3800.2.a.i 1
60.l odd 4 2 3800.2.d.d 2
84.h odd 2 1 7448.2.a.s 1
228.b odd 2 1 2888.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.a.a 1 12.b even 2 1
304.2.a.e 1 3.b odd 2 1
1216.2.a.d 1 24.h odd 2 1
1216.2.a.p 1 24.f even 2 1
1368.2.a.h 1 4.b odd 2 1
2736.2.a.p 1 1.a even 1 1 trivial
2888.2.a.f 1 228.b odd 2 1
3800.2.a.i 1 60.h even 2 1
3800.2.d.d 2 60.l odd 4 2
5776.2.a.b 1 57.d even 2 1
7448.2.a.s 1 84.h odd 2 1
7600.2.a.b 1 15.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\):

\( T_{5} - 1 \)
\( T_{7} - 3 \)
\( T_{11} + 3 \)
\( T_{13} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( -3 + T \)
$11$ \( 3 + T \)
$13$ \( 4 + T \)
$17$ \( 5 + T \)
$19$ \( -1 + T \)
$23$ \( T \)
$29$ \( 2 + T \)
$31$ \( 8 + T \)
$37$ \( 10 + T \)
$41$ \( 6 + T \)
$43$ \( -7 + T \)
$47$ \( 9 + T \)
$53$ \( -8 + T \)
$59$ \( -14 + T \)
$61$ \( 5 + T \)
$67$ \( T \)
$71$ \( 6 + T \)
$73$ \( 15 + T \)
$79$ \( -4 + T \)
$83$ \( -4 + T \)
$89$ \( T \)
$97$ \( -16 + T \)
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