Properties

Label 5733.2.a.d
Level $5733$
Weight $2$
Character orbit 5733.a
Self dual yes
Analytic conductor $45.778$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{4} + 3q^{8} + O(q^{10}) \) \( q - q^{2} - q^{4} + 3q^{8} + 3q^{11} + q^{13} - q^{16} + 7q^{17} + 7q^{19} - 3q^{22} + 6q^{23} - 5q^{25} - q^{26} + 5q^{29} - 5q^{32} - 7q^{34} + 8q^{37} - 7q^{38} + 2q^{43} - 3q^{44} - 6q^{46} + 7q^{47} + 5q^{50} - q^{52} + 3q^{53} - 5q^{58} - 7q^{59} + 7q^{61} + 7q^{64} - 3q^{67} - 7q^{68} + 5q^{71} - 14q^{73} - 8q^{74} - 7q^{76} - 6q^{79} - 2q^{86} + 9q^{88} - 6q^{92} - 7q^{94} + 14q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(13\) \(-1\)

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 5733.2.a.d 1
3.b odd 2 1 637.2.a.d 1
7.b odd 2 1 5733.2.a.c 1
7.d odd 6 2 819.2.j.b 2
21.c even 2 1 637.2.a.c 1
21.g even 6 2 91.2.e.a 2
21.h odd 6 2 637.2.e.a 2
39.d odd 2 1 8281.2.a.e 1
84.j odd 6 2 1456.2.r.g 2
273.g even 2 1 8281.2.a.f 1
273.ba even 6 2 1183.2.e.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.e.a 2 21.g even 6 2
637.2.a.c 1 21.c even 2 1
637.2.a.d 1 3.b odd 2 1
637.2.e.a 2 21.h odd 6 2
819.2.j.b 2 7.d odd 6 2
1183.2.e.b 2 273.ba even 6 2
1456.2.r.g 2 84.j odd 6 2
5733.2.a.c 1 7.b odd 2 1
5733.2.a.d 1 1.a even 1 1 trivial
8281.2.a.e 1 39.d odd 2 1
8281.2.a.f 1 273.g even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5733))\):

\( T_{2} + 1 \)
\( T_{5} \)
\( T_{11} - 3 \)
\( T_{17} - 7 \)
\( T_{19} - 7 \)
\( T_{31} \)

Hecke characteristic polynomials

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