Properties

Label 966.2.a.a
Level $966$
Weight $2$
Character orbit 966.a
Self dual yes
Analytic conductor $7.714$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.71354883526\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 4q^{10} + 2q^{11} - q^{12} + 2q^{13} - q^{14} + 4q^{15} + q^{16} + 2q^{17} - q^{18} - 2q^{19} - 4q^{20} - q^{21} - 2q^{22} + q^{23} + q^{24} + 11q^{25} - 2q^{26} - q^{27} + q^{28} - 6q^{29} - 4q^{30} - q^{32} - 2q^{33} - 2q^{34} - 4q^{35} + q^{36} + 4q^{37} + 2q^{38} - 2q^{39} + 4q^{40} - 10q^{41} + q^{42} - 10q^{43} + 2q^{44} - 4q^{45} - q^{46} - 8q^{47} - q^{48} + q^{49} - 11q^{50} - 2q^{51} + 2q^{52} + q^{54} - 8q^{55} - q^{56} + 2q^{57} + 6q^{58} + 4q^{60} - 4q^{61} + q^{63} + q^{64} - 8q^{65} + 2q^{66} + 2q^{67} + 2q^{68} - q^{69} + 4q^{70} + 8q^{71} - q^{72} - 2q^{73} - 4q^{74} - 11q^{75} - 2q^{76} + 2q^{77} + 2q^{78} - 8q^{79} - 4q^{80} + q^{81} + 10q^{82} - 6q^{83} - q^{84} - 8q^{85} + 10q^{86} + 6q^{87} - 2q^{88} + 6q^{89} + 4q^{90} + 2q^{91} + q^{92} + 8q^{94} + 8q^{95} + q^{96} - 2q^{97} - q^{98} + 2q^{99} + O(q^{100}) \)

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 −4.00000 1.00000 1.00000 −1.00000 1.00000 4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(7\) \(-1\)
\(23\) \(-1\)

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 966.2.a.a 1
3.b odd 2 1 2898.2.a.u 1
4.b odd 2 1 7728.2.a.m 1
7.b odd 2 1 6762.2.a.v 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.2.a.a 1 1.a even 1 1 trivial
2898.2.a.u 1 3.b odd 2 1
6762.2.a.v 1 7.b odd 2 1
7728.2.a.m 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(966))\):

\( T_{5} + 4 \)
\( T_{11} - 2 \)
\( T_{13} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( 4 + T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( -2 + T \)
$17$ \( -2 + T \)
$19$ \( 2 + T \)
$23$ \( -1 + T \)
$29$ \( 6 + T \)
$31$ \( T \)
$37$ \( -4 + T \)
$41$ \( 10 + T \)
$43$ \( 10 + T \)
$47$ \( 8 + T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( 4 + T \)
$67$ \( -2 + T \)
$71$ \( -8 + T \)
$73$ \( 2 + T \)
$79$ \( 8 + T \)
$83$ \( 6 + T \)
$89$ \( -6 + T \)
$97$ \( 2 + T \)
show more
show less