Properties

Label 966.6.a.b
Level $966$
Weight $6$
Character orbit 966.a
Self dual yes
Analytic conductor $154.931$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(154.930769939\)
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

\(f(q)\) \(=\) \( q + 4q^{2} + 9q^{3} + 16q^{4} + 28q^{5} + 36q^{6} + 49q^{7} + 64q^{8} + 81q^{9} + O(q^{10}) \) \( q + 4q^{2} + 9q^{3} + 16q^{4} + 28q^{5} + 36q^{6} + 49q^{7} + 64q^{8} + 81q^{9} + 112q^{10} - 15q^{11} + 144q^{12} - 1066q^{13} + 196q^{14} + 252q^{15} + 256q^{16} - 80q^{17} + 324q^{18} - 1319q^{19} + 448q^{20} + 441q^{21} - 60q^{22} + 529q^{23} + 576q^{24} - 2341q^{25} - 4264q^{26} + 729q^{27} + 784q^{28} - 3586q^{29} + 1008q^{30} - 7850q^{31} + 1024q^{32} - 135q^{33} - 320q^{34} + 1372q^{35} + 1296q^{36} + 5074q^{37} - 5276q^{38} - 9594q^{39} + 1792q^{40} - 17627q^{41} + 1764q^{42} + 10392q^{43} - 240q^{44} + 2268q^{45} + 2116q^{46} - 11805q^{47} + 2304q^{48} + 2401q^{49} - 9364q^{50} - 720q^{51} - 17056q^{52} - 345q^{53} + 2916q^{54} - 420q^{55} + 3136q^{56} - 11871q^{57} - 14344q^{58} - 31347q^{59} + 4032q^{60} - 5019q^{61} - 31400q^{62} + 3969q^{63} + 4096q^{64} - 29848q^{65} - 540q^{66} - 26552q^{67} - 1280q^{68} + 4761q^{69} + 5488q^{70} - 23492q^{71} + 5184q^{72} - 5356q^{73} + 20296q^{74} - 21069q^{75} - 21104q^{76} - 735q^{77} - 38376q^{78} + 99870q^{79} + 7168q^{80} + 6561q^{81} - 70508q^{82} + 47482q^{83} + 7056q^{84} - 2240q^{85} + 41568q^{86} - 32274q^{87} - 960q^{88} - 58182q^{89} + 9072q^{90} - 52234q^{91} + 8464q^{92} - 70650q^{93} - 47220q^{94} - 36932q^{95} + 9216q^{96} + 72722q^{97} + 9604q^{98} - 1215q^{99} + O(q^{100}) \)

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
4.00000 9.00000 16.0000 28.0000 36.0000 49.0000 64.0000 81.0000 112.000
\(n\): 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 966.6.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.6.a.b 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 28 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(966))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -4 + T \)
$3$ \( -9 + T \)
$5$ \( -28 + T \)
$7$ \( -49 + T \)
$11$ \( 15 + T \)
$13$ \( 1066 + T \)
$17$ \( 80 + T \)
$19$ \( 1319 + T \)
$23$ \( -529 + T \)
$29$ \( 3586 + T \)
$31$ \( 7850 + T \)
$37$ \( -5074 + T \)
$41$ \( 17627 + T \)
$43$ \( -10392 + T \)
$47$ \( 11805 + T \)
$53$ \( 345 + T \)
$59$ \( 31347 + T \)
$61$ \( 5019 + T \)
$67$ \( 26552 + T \)
$71$ \( 23492 + T \)
$73$ \( 5356 + T \)
$79$ \( -99870 + T \)
$83$ \( -47482 + T \)
$89$ \( 58182 + T \)
$97$ \( -72722 + T \)
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