Properties

Label 5850.2.a.bj
Level $5850$
Weight $2$
Character orbit 5850.a
Self dual yes
Analytic conductor $46.712$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.7124851824\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 2q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - 2q^{7} + q^{8} - 2q^{11} + q^{13} - 2q^{14} + q^{16} + 2q^{17} - 4q^{19} - 2q^{22} + q^{26} - 2q^{28} - 4q^{29} + 8q^{31} + q^{32} + 2q^{34} - 6q^{37} - 4q^{38} + 6q^{41} - 4q^{43} - 2q^{44} - 8q^{47} - 3q^{49} + q^{52} + 2q^{53} - 2q^{56} - 4q^{58} - 10q^{59} - 14q^{61} + 8q^{62} + q^{64} + 16q^{67} + 2q^{68} + 4q^{71} - 8q^{73} - 6q^{74} - 4q^{76} + 4q^{77} - 8q^{79} + 6q^{82} + 12q^{83} - 4q^{86} - 2q^{88} - 6q^{89} - 2q^{91} - 8q^{94} - 12q^{97} - 3q^{98} + O(q^{100}) \)

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 −2.00000 1.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(13\) \(-1\)

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 5850.2.a.bj 1
3.b odd 2 1 1950.2.a.c 1
5.b even 2 1 5850.2.a.t 1
5.c odd 4 2 1170.2.e.a 2
15.d odd 2 1 1950.2.a.z 1
15.e even 4 2 390.2.e.c 2
60.l odd 4 2 3120.2.l.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
390.2.e.c 2 15.e even 4 2
1170.2.e.a 2 5.c odd 4 2
1950.2.a.c 1 3.b odd 2 1
1950.2.a.z 1 15.d odd 2 1
3120.2.l.g 2 60.l odd 4 2
5850.2.a.t 1 5.b even 2 1
5850.2.a.bj 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5850))\):

\( T_{7} + 2 \)
\( T_{11} + 2 \)
\( T_{17} - 2 \)
\( T_{23} \)
\( T_{31} - 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( 2 + T \)
$13$ \( -1 + T \)
$17$ \( -2 + T \)
$19$ \( 4 + T \)
$23$ \( T \)
$29$ \( 4 + T \)
$31$ \( -8 + T \)
$37$ \( 6 + T \)
$41$ \( -6 + T \)
$43$ \( 4 + T \)
$47$ \( 8 + T \)
$53$ \( -2 + T \)
$59$ \( 10 + T \)
$61$ \( 14 + T \)
$67$ \( -16 + T \)
$71$ \( -4 + T \)
$73$ \( 8 + T \)
$79$ \( 8 + T \)
$83$ \( -12 + T \)
$89$ \( 6 + T \)
$97$ \( 12 + T \)
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