Properties

Label 7942.2.a.c
Level $7942$
Weight $2$
Character orbit 7942.a
Self dual yes
Analytic conductor $63.417$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7942.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.4171892853\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - 2 q^{3} + q^{4} + q^{5} + 2 q^{6} - 3 q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - 2 q^{3} + q^{4} + q^{5} + 2 q^{6} - 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{11} - 2 q^{12} - 4 q^{13} + 3 q^{14} - 2 q^{15} + q^{16} - 4 q^{17} - q^{18} + q^{20} + 6 q^{21} + q^{22} + 4 q^{23} + 2 q^{24} - 4 q^{25} + 4 q^{26} + 4 q^{27} - 3 q^{28} - 10 q^{29} + 2 q^{30} - 4 q^{31} - q^{32} + 2 q^{33} + 4 q^{34} - 3 q^{35} + q^{36} - 3 q^{37} + 8 q^{39} - q^{40} - 6 q^{41} - 6 q^{42} - 4 q^{43} - q^{44} + q^{45} - 4 q^{46} + 6 q^{47} - 2 q^{48} + 2 q^{49} + 4 q^{50} + 8 q^{51} - 4 q^{52} + q^{53} - 4 q^{54} - q^{55} + 3 q^{56} + 10 q^{58} - 12 q^{59} - 2 q^{60} + 12 q^{61} + 4 q^{62} - 3 q^{63} + q^{64} - 4 q^{65} - 2 q^{66} - 12 q^{67} - 4 q^{68} - 8 q^{69} + 3 q^{70} - 14 q^{71} - q^{72} + 6 q^{73} + 3 q^{74} + 8 q^{75} + 3 q^{77} - 8 q^{78} - 17 q^{79} + q^{80} - 11 q^{81} + 6 q^{82} - 13 q^{83} + 6 q^{84} - 4 q^{85} + 4 q^{86} + 20 q^{87} + q^{88} + 2 q^{89} - q^{90} + 12 q^{91} + 4 q^{92} + 8 q^{93} - 6 q^{94} + 2 q^{96} - 5 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 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
−1.00000 −2.00000 1.00000 1.00000 2.00000 −3.00000 −1.00000 1.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(11\) \(1\)
\(19\) \(-1\)

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 7942.2.a.c 1
19.b odd 2 1 7942.2.a.s 1
19.d odd 6 2 418.2.e.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
418.2.e.a 2 19.d odd 6 2
7942.2.a.c 1 1.a even 1 1 trivial
7942.2.a.s 1 19.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7942))\):

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{5} - 1 \) Copy content Toggle raw display
\( T_{13} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T + 1 \) Copy content Toggle raw display
$13$ \( T + 4 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 4 \) Copy content Toggle raw display
$29$ \( T + 10 \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T + 3 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T + 4 \) Copy content Toggle raw display
$47$ \( T - 6 \) Copy content Toggle raw display
$53$ \( T - 1 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T - 12 \) Copy content Toggle raw display
$67$ \( T + 12 \) Copy content Toggle raw display
$71$ \( T + 14 \) Copy content Toggle raw display
$73$ \( T - 6 \) Copy content Toggle raw display
$79$ \( T + 17 \) Copy content Toggle raw display
$83$ \( T + 13 \) Copy content Toggle raw display
$89$ \( T - 2 \) Copy content Toggle raw display
$97$ \( T + 5 \) Copy content Toggle raw display
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