Properties

Label 966.4.a.a
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

\(f(q)\) \(=\) \( q - 2 q^{2} + 3 q^{3} + 4 q^{4} - 6 q^{5} - 6 q^{6} + 7 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 3 q^{3} + 4 q^{4} - 6 q^{5} - 6 q^{6} + 7 q^{7} - 8 q^{8} + 9 q^{9} + 12 q^{10} + 48 q^{11} + 12 q^{12} + 38 q^{13} - 14 q^{14} - 18 q^{15} + 16 q^{16} + 114 q^{17} - 18 q^{18} + 56 q^{19} - 24 q^{20} + 21 q^{21} - 96 q^{22} - 23 q^{23} - 24 q^{24} - 89 q^{25} - 76 q^{26} + 27 q^{27} + 28 q^{28} - 162 q^{29} + 36 q^{30} - 16 q^{31} - 32 q^{32} + 144 q^{33} - 228 q^{34} - 42 q^{35} + 36 q^{36} - 46 q^{37} - 112 q^{38} + 114 q^{39} + 48 q^{40} - 342 q^{41} - 42 q^{42} + 248 q^{43} + 192 q^{44} - 54 q^{45} + 46 q^{46} - 24 q^{47} + 48 q^{48} + 49 q^{49} + 178 q^{50} + 342 q^{51} + 152 q^{52} + 426 q^{53} - 54 q^{54} - 288 q^{55} - 56 q^{56} + 168 q^{57} + 324 q^{58} - 852 q^{59} - 72 q^{60} + 338 q^{61} + 32 q^{62} + 63 q^{63} + 64 q^{64} - 228 q^{65} - 288 q^{66} + 488 q^{67} + 456 q^{68} - 69 q^{69} + 84 q^{70} + 336 q^{71} - 72 q^{72} + 362 q^{73} + 92 q^{74} - 267 q^{75} + 224 q^{76} + 336 q^{77} - 228 q^{78} + 1184 q^{79} - 96 q^{80} + 81 q^{81} + 684 q^{82} - 336 q^{83} + 84 q^{84} - 684 q^{85} - 496 q^{86} - 486 q^{87} - 384 q^{88} - 78 q^{89} + 108 q^{90} + 266 q^{91} - 92 q^{92} - 48 q^{93} + 48 q^{94} - 336 q^{95} - 96 q^{96} + 746 q^{97} - 98 q^{98} + 432 q^{99}+O(q^{100}) \) 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 −6.00000 −6.00000 7.00000 −8.00000 9.00000 12.0000
\(n\): 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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.4.a.a 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 6 \) 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
$5$ \( T + 6 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T - 48 \) Copy content Toggle raw display
$13$ \( T - 38 \) Copy content Toggle raw display
$17$ \( T - 114 \) Copy content Toggle raw display
$19$ \( T - 56 \) Copy content Toggle raw display
$23$ \( T + 23 \) Copy content Toggle raw display
$29$ \( T + 162 \) Copy content Toggle raw display
$31$ \( T + 16 \) Copy content Toggle raw display
$37$ \( T + 46 \) Copy content Toggle raw display
$41$ \( T + 342 \) Copy content Toggle raw display
$43$ \( T - 248 \) Copy content Toggle raw display
$47$ \( T + 24 \) Copy content Toggle raw display
$53$ \( T - 426 \) Copy content Toggle raw display
$59$ \( T + 852 \) Copy content Toggle raw display
$61$ \( T - 338 \) Copy content Toggle raw display
$67$ \( T - 488 \) Copy content Toggle raw display
$71$ \( T - 336 \) Copy content Toggle raw display
$73$ \( T - 362 \) Copy content Toggle raw display
$79$ \( T - 1184 \) Copy content Toggle raw display
$83$ \( T + 336 \) Copy content Toggle raw display
$89$ \( T + 78 \) Copy content Toggle raw display
$97$ \( T - 746 \) Copy content Toggle raw display
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