Properties

Label 1950.2.a.g
Level $1950$
Weight $2$
Character orbit 1950.a
Self dual yes
Analytic conductor $15.571$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} - 4 q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{3} + q^{4} - q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{11} + q^{12} - q^{13} + 4 q^{14} + q^{16} - 4 q^{17} - q^{18} + 2 q^{19} - 4 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + q^{26} + q^{27} - 4 q^{28} - 2 q^{29} - 4 q^{31} - q^{32} + 2 q^{33} + 4 q^{34} + q^{36} + 6 q^{37} - 2 q^{38} - q^{39} - 6 q^{41} + 4 q^{42} - 8 q^{43} + 2 q^{44} - 6 q^{46} - 8 q^{47} + q^{48} + 9 q^{49} - 4 q^{51} - q^{52} - 10 q^{53} - q^{54} + 4 q^{56} + 2 q^{57} + 2 q^{58} - 14 q^{59} + 10 q^{61} + 4 q^{62} - 4 q^{63} + q^{64} - 2 q^{66} - 4 q^{67} - 4 q^{68} + 6 q^{69} + 8 q^{71} - q^{72} - 10 q^{73} - 6 q^{74} + 2 q^{76} - 8 q^{77} + q^{78} - 8 q^{79} + q^{81} + 6 q^{82} - 12 q^{83} - 4 q^{84} + 8 q^{86} - 2 q^{87} - 2 q^{88} - 18 q^{89} + 4 q^{91} + 6 q^{92} - 4 q^{93} + 8 q^{94} - q^{96} - 6 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 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 −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.g 1
3.b odd 2 1 5850.2.a.bd 1
5.b even 2 1 1950.2.a.u 1
5.c odd 4 2 390.2.e.b 2
15.d odd 2 1 5850.2.a.x 1
15.e even 4 2 1170.2.e.b 2
20.e even 4 2 3120.2.l.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
390.2.e.b 2 5.c odd 4 2
1170.2.e.b 2 15.e even 4 2
1950.2.a.g 1 1.a even 1 1 trivial
1950.2.a.u 1 5.b even 2 1
3120.2.l.h 2 20.e even 4 2
5850.2.a.x 1 15.d odd 2 1
5850.2.a.bd 1 3.b odd 2 1

Hecke kernels

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

\( T_{7} + 4 \) Copy content Toggle raw display
\( T_{11} - 2 \) Copy content Toggle raw display
\( T_{17} + 4 \) Copy content Toggle raw display
\( T_{23} - 6 \) Copy content Toggle raw display
\( T_{31} + 4 \) 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
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T - 6 \) Copy content Toggle raw display
$29$ \( T + 2 \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T - 6 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T + 8 \) Copy content Toggle raw display
$53$ \( T + 10 \) Copy content Toggle raw display
$59$ \( T + 14 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T - 8 \) Copy content Toggle raw display
$73$ \( T + 10 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T + 18 \) Copy content Toggle raw display
$97$ \( T + 6 \) Copy content Toggle raw display
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