Properties

Label 1950.2.a.a
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{6} - 3q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} + q^{6} - 3q^{7} - q^{8} + q^{9} - 3q^{11} - q^{12} - q^{13} + 3q^{14} + q^{16} - 3q^{17} - q^{18} + 3q^{21} + 3q^{22} - 4q^{23} + q^{24} + q^{26} - q^{27} - 3q^{28} + 5q^{29} - 3q^{31} - q^{32} + 3q^{33} + 3q^{34} + q^{36} + 12q^{37} + q^{39} + 2q^{41} - 3q^{42} - 4q^{43} - 3q^{44} + 4q^{46} - 3q^{47} - q^{48} + 2q^{49} + 3q^{51} - q^{52} - 9q^{53} + q^{54} + 3q^{56} - 5q^{58} + 15q^{59} - 3q^{61} + 3q^{62} - 3q^{63} + q^{64} - 3q^{66} + 7q^{67} - 3q^{68} + 4q^{69} - 8q^{71} - q^{72} + 16q^{73} - 12q^{74} + 9q^{77} - q^{78} + q^{81} - 2q^{82} + q^{83} + 3q^{84} + 4q^{86} - 5q^{87} + 3q^{88} + 3q^{91} - 4q^{92} + 3q^{93} + 3q^{94} + q^{96} + 2q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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 −3.00000 −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.a 1
3.b odd 2 1 5850.2.a.bf 1
5.b even 2 1 1950.2.a.bb yes 1
5.c odd 4 2 1950.2.e.j 2
15.d odd 2 1 5850.2.a.w 1
15.e even 4 2 5850.2.e.z 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1950.2.a.a 1 1.a even 1 1 trivial
1950.2.a.bb yes 1 5.b even 2 1
1950.2.e.j 2 5.c odd 4 2
5850.2.a.w 1 15.d odd 2 1
5850.2.a.bf 1 3.b odd 2 1
5850.2.e.z 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\):

\( T_{7} + 3 \)
\( T_{11} + 3 \)
\( T_{17} + 3 \)
\( T_{23} + 4 \)
\( T_{31} + 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( 3 + T \)
$11$ \( 3 + T \)
$13$ \( 1 + T \)
$17$ \( 3 + T \)
$19$ \( T \)
$23$ \( 4 + T \)
$29$ \( -5 + T \)
$31$ \( 3 + T \)
$37$ \( -12 + T \)
$41$ \( -2 + T \)
$43$ \( 4 + T \)
$47$ \( 3 + T \)
$53$ \( 9 + T \)
$59$ \( -15 + T \)
$61$ \( 3 + T \)
$67$ \( -7 + T \)
$71$ \( 8 + T \)
$73$ \( -16 + T \)
$79$ \( T \)
$83$ \( -1 + T \)
$89$ \( T \)
$97$ \( -2 + T \)
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