Properties

Label 7938.2.a.n
Level $7938$
Weight $2$
Character orbit 7938.a
Self dual yes
Analytic conductor $63.385$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7938.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.3852491245\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 162)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 3 q^{5} - q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} + q^{13} + q^{16} + 3 q^{17} + 4 q^{19} + 3 q^{20} + 4 q^{25} - q^{26} + 9 q^{29} + 4 q^{31} - q^{32} - 3 q^{34} - q^{37} - 4 q^{38} - 3 q^{40} - 6 q^{41} + 8 q^{43} + 12 q^{47} - 4 q^{50} + q^{52} - 6 q^{53} - 9 q^{58} + q^{61} - 4 q^{62} + q^{64} + 3 q^{65} - 4 q^{67} + 3 q^{68} - 12 q^{71} - 11 q^{73} + q^{74} + 4 q^{76} - 16 q^{79} + 3 q^{80} + 6 q^{82} + 12 q^{83} + 9 q^{85} - 8 q^{86} + 3 q^{89} - 12 q^{94} + 12 q^{95} - 2 q^{97}+O(q^{100}) \) 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 0 1.00000 3.00000 0 0 −1.00000 0 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 7938.2.a.n 1
3.b odd 2 1 7938.2.a.s 1
7.b odd 2 1 162.2.a.a 1
21.c even 2 1 162.2.a.d yes 1
28.d even 2 1 1296.2.a.c 1
35.c odd 2 1 4050.2.a.bh 1
35.f even 4 2 4050.2.c.g 2
56.e even 2 1 5184.2.a.bd 1
56.h odd 2 1 5184.2.a.y 1
63.l odd 6 2 162.2.c.d 2
63.o even 6 2 162.2.c.a 2
84.h odd 2 1 1296.2.a.l 1
105.g even 2 1 4050.2.a.r 1
105.k odd 4 2 4050.2.c.n 2
168.e odd 2 1 5184.2.a.h 1
168.i even 2 1 5184.2.a.c 1
252.s odd 6 2 1296.2.i.b 2
252.bi even 6 2 1296.2.i.n 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
162.2.a.a 1 7.b odd 2 1
162.2.a.d yes 1 21.c even 2 1
162.2.c.a 2 63.o even 6 2
162.2.c.d 2 63.l odd 6 2
1296.2.a.c 1 28.d even 2 1
1296.2.a.l 1 84.h odd 2 1
1296.2.i.b 2 252.s odd 6 2
1296.2.i.n 2 252.bi even 6 2
4050.2.a.r 1 105.g even 2 1
4050.2.a.bh 1 35.c odd 2 1
4050.2.c.g 2 35.f even 4 2
4050.2.c.n 2 105.k odd 4 2
5184.2.a.c 1 168.i even 2 1
5184.2.a.h 1 168.e odd 2 1
5184.2.a.y 1 56.h odd 2 1
5184.2.a.bd 1 56.e even 2 1
7938.2.a.n 1 1.a even 1 1 trivial
7938.2.a.s 1 3.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7938))\):

\( T_{5} - 3 \) Copy content Toggle raw display
\( T_{11} \) Copy content Toggle raw display
\( T_{13} - 1 \) Copy content Toggle raw display
\( T_{17} - 3 \) Copy content Toggle raw display
\( T_{23} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 1 \) Copy content Toggle raw display
$17$ \( T - 3 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T - 9 \) Copy content Toggle raw display
$31$ \( T - 4 \) Copy content Toggle raw display
$37$ \( T + 1 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T - 8 \) Copy content Toggle raw display
$47$ \( T - 12 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 1 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T + 12 \) Copy content Toggle raw display
$73$ \( T + 11 \) Copy content Toggle raw display
$79$ \( T + 16 \) Copy content Toggle raw display
$83$ \( T - 12 \) Copy content Toggle raw display
$89$ \( T - 3 \) Copy content Toggle raw display
$97$ \( T + 2 \) Copy content Toggle raw display
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