Properties

Label 1950.2.a.s
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 4q^{11} - q^{12} + q^{13} + q^{16} + q^{18} + q^{19} + 4q^{22} - 4q^{23} - q^{24} + q^{26} - q^{27} - 3q^{29} + 4q^{31} + q^{32} - 4q^{33} + q^{36} + 5q^{37} + q^{38} - q^{39} + 9q^{41} - 2q^{43} + 4q^{44} - 4q^{46} + 3q^{47} - q^{48} - 7q^{49} + q^{52} - q^{53} - q^{54} - q^{57} - 3q^{58} + 10q^{59} + 4q^{61} + 4q^{62} + q^{64} - 4q^{66} + 9q^{67} + 4q^{69} + 7q^{71} + q^{72} - 4q^{73} + 5q^{74} + q^{76} - q^{78} + 11q^{79} + q^{81} + 9q^{82} - 6q^{83} - 2q^{86} + 3q^{87} + 4q^{88} + 10q^{89} - 4q^{92} - 4q^{93} + 3q^{94} - q^{96} + 12q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

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 0 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.s yes 1
3.b odd 2 1 5850.2.a.l 1
5.b even 2 1 1950.2.a.j 1
5.c odd 4 2 1950.2.e.h 2
15.d odd 2 1 5850.2.a.bp 1
15.e even 4 2 5850.2.e.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1950.2.a.j 1 5.b even 2 1
1950.2.a.s yes 1 1.a even 1 1 trivial
1950.2.e.h 2 5.c odd 4 2
5850.2.a.l 1 3.b odd 2 1
5850.2.a.bp 1 15.d odd 2 1
5850.2.e.f 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( -1 + T \)
$23$ \( 4 + T \)
$29$ \( 3 + T \)
$31$ \( -4 + T \)
$37$ \( -5 + T \)
$41$ \( -9 + T \)
$43$ \( 2 + T \)
$47$ \( -3 + T \)
$53$ \( 1 + T \)
$59$ \( -10 + T \)
$61$ \( -4 + T \)
$67$ \( -9 + T \)
$71$ \( -7 + T \)
$73$ \( 4 + T \)
$79$ \( -11 + T \)
$83$ \( 6 + T \)
$89$ \( -10 + T \)
$97$ \( -12 + T \)
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