Properties

Label 950.2.a.c
Level $950$
Weight $2$
Character orbit 950.a
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 3q^{3} + q^{4} - 3q^{6} + 5q^{7} - q^{8} + 6q^{9} + O(q^{10}) \) \( q - q^{2} + 3q^{3} + q^{4} - 3q^{6} + 5q^{7} - q^{8} + 6q^{9} - 4q^{11} + 3q^{12} + q^{13} - 5q^{14} + q^{16} + 3q^{17} - 6q^{18} + q^{19} + 15q^{21} + 4q^{22} - 7q^{23} - 3q^{24} - q^{26} + 9q^{27} + 5q^{28} - 3q^{29} - 2q^{31} - q^{32} - 12q^{33} - 3q^{34} + 6q^{36} + 2q^{37} - q^{38} + 3q^{39} - 6q^{41} - 15q^{42} - 6q^{43} - 4q^{44} + 7q^{46} + 3q^{48} + 18q^{49} + 9q^{51} + q^{52} + 13q^{53} - 9q^{54} - 5q^{56} + 3q^{57} + 3q^{58} - 9q^{59} - 12q^{61} + 2q^{62} + 30q^{63} + q^{64} + 12q^{66} + 3q^{67} + 3q^{68} - 21q^{69} - 6q^{72} - 11q^{73} - 2q^{74} + q^{76} - 20q^{77} - 3q^{78} - 2q^{79} + 9q^{81} + 6q^{82} + 10q^{83} + 15q^{84} + 6q^{86} - 9q^{87} + 4q^{88} + 2q^{89} + 5q^{91} - 7q^{92} - 6q^{93} - 3q^{96} + 2q^{97} - 18q^{98} - 24q^{99} + O(q^{100}) \)

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 3.00000 1.00000 0 −3.00000 5.00000 −1.00000 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(1\)
\(19\) \(-1\)

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 950.2.a.c 1
3.b odd 2 1 8550.2.a.bm 1
4.b odd 2 1 7600.2.a.a 1
5.b even 2 1 190.2.a.b 1
5.c odd 4 2 950.2.b.a 2
15.d odd 2 1 1710.2.a.g 1
20.d odd 2 1 1520.2.a.j 1
35.c odd 2 1 9310.2.a.u 1
40.e odd 2 1 6080.2.a.b 1
40.f even 2 1 6080.2.a.x 1
95.d odd 2 1 3610.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.b 1 5.b even 2 1
950.2.a.c 1 1.a even 1 1 trivial
950.2.b.a 2 5.c odd 4 2
1520.2.a.j 1 20.d odd 2 1
1710.2.a.g 1 15.d odd 2 1
3610.2.a.e 1 95.d odd 2 1
6080.2.a.b 1 40.e odd 2 1
6080.2.a.x 1 40.f even 2 1
7600.2.a.a 1 4.b odd 2 1
8550.2.a.bm 1 3.b odd 2 1
9310.2.a.u 1 35.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(950))\):

\( T_{3} - 3 \)
\( T_{7} - 5 \)
\( T_{11} + 4 \)

Hecke characteristic polynomials

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