Properties

Label 5850.2.a.k
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 1950)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} + 5q^{11} - q^{13} + q^{14} + q^{16} - 5q^{17} - 5q^{22} + q^{26} - q^{28} + 7q^{29} - 9q^{31} - q^{32} + 5q^{34} - 8q^{37} + 2q^{41} + 8q^{43} + 5q^{44} + 9q^{47} - 6q^{49} - q^{52} - 11q^{53} + q^{56} - 7q^{58} - q^{59} - 7q^{61} + 9q^{62} + q^{64} - 15q^{67} - 5q^{68} + 8q^{71} + 4q^{73} + 8q^{74} - 5q^{77} - 4q^{79} - 2q^{82} + 9q^{83} - 8q^{86} - 5q^{88} - 16q^{89} + q^{91} - 9q^{94} + 2q^{97} + 6q^{98} + O(q^{100}) \)

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 −1.00000 −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.k 1
3.b odd 2 1 1950.2.a.p yes 1
5.b even 2 1 5850.2.a.bu 1
5.c odd 4 2 5850.2.e.be 2
15.d odd 2 1 1950.2.a.l 1
15.e even 4 2 1950.2.e.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1950.2.a.l 1 15.d odd 2 1
1950.2.a.p yes 1 3.b odd 2 1
1950.2.e.a 2 15.e even 4 2
5850.2.a.k 1 1.a even 1 1 trivial
5850.2.a.bu 1 5.b even 2 1
5850.2.e.be 2 5.c odd 4 2

Hecke kernels

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

\( T_{7} + 1 \)
\( T_{11} - 5 \)
\( T_{17} + 5 \)
\( T_{23} \)
\( T_{31} + 9 \)

Hecke characteristic polynomials

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