Properties

Label 1950.2.a.f
Level $1950$
Weight $2$
Character orbit 1950.a
Self dual yes
Analytic conductor $15.571$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} + q^{12} + q^{13} + 4q^{14} + q^{16} - q^{18} + 5q^{19} - 4q^{21} - q^{24} - q^{26} + q^{27} - 4q^{28} + 3q^{29} - 4q^{31} - q^{32} + q^{36} - 7q^{37} - 5q^{38} + q^{39} + 3q^{41} + 4q^{42} + 2q^{43} + 9q^{47} + q^{48} + 9q^{49} + q^{52} + 9q^{53} - q^{54} + 4q^{56} + 5q^{57} - 3q^{58} + 6q^{59} + 8q^{61} + 4q^{62} - 4q^{63} + q^{64} + 5q^{67} - 3q^{71} - q^{72} - 4q^{73} + 7q^{74} + 5q^{76} - q^{78} + 11q^{79} + q^{81} - 3q^{82} - 6q^{83} - 4q^{84} - 2q^{86} + 3q^{87} + 6q^{89} - 4q^{91} - 4q^{93} - 9q^{94} - q^{96} + 8q^{97} - 9q^{98} + O(q^{100}) \)

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 1.00000 1.00000 0 −1.00000 −4.00000 −1.00000 1.00000 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 1950.2.a.f 1
3.b odd 2 1 5850.2.a.be 1
5.b even 2 1 1950.2.a.t yes 1
5.c odd 4 2 1950.2.e.c 2
15.d odd 2 1 5850.2.a.y 1
15.e even 4 2 5850.2.e.s 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1950.2.a.f 1 1.a even 1 1 trivial
1950.2.a.t yes 1 5.b even 2 1
1950.2.e.c 2 5.c odd 4 2
5850.2.a.y 1 15.d odd 2 1
5850.2.a.be 1 3.b odd 2 1
5850.2.e.s 2 15.e even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\):

\( T_{7} + 4 \)
\( T_{11} \)
\( T_{17} \)
\( T_{23} \)
\( T_{31} + 4 \)

Hecke characteristic polynomials

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