Properties

Label 966.4.a.b
Level $966$
Weight $4$
Character orbit 966.a
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 9 q^{5} - 6 q^{6} + 7 q^{7} + 8 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 9 q^{5} - 6 q^{6} + 7 q^{7} + 8 q^{8} + 9 q^{9} - 18 q^{10} - 12 q^{11} - 12 q^{12} + 11 q^{13} + 14 q^{14} + 27 q^{15} + 16 q^{16} + 96 q^{17} + 18 q^{18} - 40 q^{19} - 36 q^{20} - 21 q^{21} - 24 q^{22} - 23 q^{23} - 24 q^{24} - 44 q^{25} + 22 q^{26} - 27 q^{27} + 28 q^{28} - 231 q^{29} + 54 q^{30} - 94 q^{31} + 32 q^{32} + 36 q^{33} + 192 q^{34} - 63 q^{35} + 36 q^{36} + 47 q^{37} - 80 q^{38} - 33 q^{39} - 72 q^{40} - 27 q^{41} - 42 q^{42} + 479 q^{43} - 48 q^{44} - 81 q^{45} - 46 q^{46} + 423 q^{47} - 48 q^{48} + 49 q^{49} - 88 q^{50} - 288 q^{51} + 44 q^{52} + 516 q^{53} - 54 q^{54} + 108 q^{55} + 56 q^{56} + 120 q^{57} - 462 q^{58} + 882 q^{59} + 108 q^{60} + 842 q^{61} - 188 q^{62} + 63 q^{63} + 64 q^{64} - 99 q^{65} + 72 q^{66} - 844 q^{67} + 384 q^{68} + 69 q^{69} - 126 q^{70} + 654 q^{71} + 72 q^{72} - 496 q^{73} + 94 q^{74} + 132 q^{75} - 160 q^{76} - 84 q^{77} - 66 q^{78} + 260 q^{79} - 144 q^{80} + 81 q^{81} - 54 q^{82} - 156 q^{83} - 84 q^{84} - 864 q^{85} + 958 q^{86} + 693 q^{87} - 96 q^{88} - 414 q^{89} - 162 q^{90} + 77 q^{91} - 92 q^{92} + 282 q^{93} + 846 q^{94} + 360 q^{95} - 96 q^{96} + 1343 q^{97} + 98 q^{98} - 108 q^{99}+O(q^{100}) \) 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
2.00000 −3.00000 4.00000 −9.00000 −6.00000 7.00000 8.00000 9.00000 −18.0000
\(n\): 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 966.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.4.a.b 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 9 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(966))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T + 3 \) Copy content Toggle raw display
$5$ \( T + 9 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T + 12 \) Copy content Toggle raw display
$13$ \( T - 11 \) Copy content Toggle raw display
$17$ \( T - 96 \) Copy content Toggle raw display
$19$ \( T + 40 \) Copy content Toggle raw display
$23$ \( T + 23 \) Copy content Toggle raw display
$29$ \( T + 231 \) Copy content Toggle raw display
$31$ \( T + 94 \) Copy content Toggle raw display
$37$ \( T - 47 \) Copy content Toggle raw display
$41$ \( T + 27 \) Copy content Toggle raw display
$43$ \( T - 479 \) Copy content Toggle raw display
$47$ \( T - 423 \) Copy content Toggle raw display
$53$ \( T - 516 \) Copy content Toggle raw display
$59$ \( T - 882 \) Copy content Toggle raw display
$61$ \( T - 842 \) Copy content Toggle raw display
$67$ \( T + 844 \) Copy content Toggle raw display
$71$ \( T - 654 \) Copy content Toggle raw display
$73$ \( T + 496 \) Copy content Toggle raw display
$79$ \( T - 260 \) Copy content Toggle raw display
$83$ \( T + 156 \) Copy content Toggle raw display
$89$ \( T + 414 \) Copy content Toggle raw display
$97$ \( T - 1343 \) Copy content Toggle raw display
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