Properties

Label 1950.2.a.k
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: no (minimal twist has level 390)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4 q^{11} + q^{12} - q^{13} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} - 4 q^{22} - 8 q^{23} - q^{24} + q^{26} + q^{27} + 6 q^{29} - 8 q^{31} - q^{32} + 4 q^{33} - 6 q^{34} + q^{36} + 10 q^{37} - 4 q^{38} - q^{39} - 6 q^{41} - 4 q^{43} + 4 q^{44} + 8 q^{46} + q^{48} - 7 q^{49} + 6 q^{51} - q^{52} + 10 q^{53} - q^{54} + 4 q^{57} - 6 q^{58} + 4 q^{59} - 2 q^{61} + 8 q^{62} + q^{64} - 4 q^{66} + 12 q^{67} + 6 q^{68} - 8 q^{69} + 16 q^{71} - q^{72} - 2 q^{73} - 10 q^{74} + 4 q^{76} + q^{78} - 16 q^{79} + q^{81} + 6 q^{82} + 12 q^{83} + 4 q^{86} + 6 q^{87} - 4 q^{88} + 10 q^{89} - 8 q^{92} - 8 q^{93} - q^{96} + 6 q^{97} + 7 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.k 1
3.b odd 2 1 5850.2.a.bo 1
5.b even 2 1 390.2.a.f 1
5.c odd 4 2 1950.2.e.g 2
15.d odd 2 1 1170.2.a.a 1
15.e even 4 2 5850.2.e.e 2
20.d odd 2 1 3120.2.a.w 1
60.h even 2 1 9360.2.a.p 1
65.d even 2 1 5070.2.a.a 1
65.g odd 4 2 5070.2.b.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
390.2.a.f 1 5.b even 2 1
1170.2.a.a 1 15.d odd 2 1
1950.2.a.k 1 1.a even 1 1 trivial
1950.2.e.g 2 5.c odd 4 2
3120.2.a.w 1 20.d odd 2 1
5070.2.a.a 1 65.d even 2 1
5070.2.b.d 2 65.g odd 4 2
5850.2.a.bo 1 3.b odd 2 1
5850.2.e.e 2 15.e even 4 2
9360.2.a.p 1 60.h even 2 1

Hecke kernels

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

\( T_{7} \) Copy content Toggle raw display
\( T_{11} - 4 \) Copy content Toggle raw display
\( T_{17} - 6 \) Copy content Toggle raw display
\( T_{23} + 8 \) Copy content Toggle raw display
\( T_{31} + 8 \) Copy content Toggle raw display

Hecke characteristic polynomials

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