Properties

Label 931.4.a.a
Level $931$
Weight $4$
Character orbit 931.a
Self dual yes
Analytic conductor $54.931$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 931.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.9307782153\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 3q^{2} + 5q^{3} + q^{4} + 12q^{5} - 15q^{6} + 21q^{8} - 2q^{9} + O(q^{10}) \) \( q - 3q^{2} + 5q^{3} + q^{4} + 12q^{5} - 15q^{6} + 21q^{8} - 2q^{9} - 36q^{10} - 54q^{11} + 5q^{12} - 11q^{13} + 60q^{15} - 71q^{16} + 93q^{17} + 6q^{18} - 19q^{19} + 12q^{20} + 162q^{22} + 183q^{23} + 105q^{24} + 19q^{25} + 33q^{26} - 145q^{27} - 249q^{29} - 180q^{30} - 56q^{31} + 45q^{32} - 270q^{33} - 279q^{34} - 2q^{36} - 250q^{37} + 57q^{38} - 55q^{39} + 252q^{40} - 240q^{41} - 196q^{43} - 54q^{44} - 24q^{45} - 549q^{46} + 168q^{47} - 355q^{48} - 57q^{50} + 465q^{51} - 11q^{52} + 435q^{53} + 435q^{54} - 648q^{55} - 95q^{57} + 747q^{58} - 195q^{59} + 60q^{60} + 358q^{61} + 168q^{62} + 433q^{64} - 132q^{65} + 810q^{66} - 961q^{67} + 93q^{68} + 915q^{69} - 246q^{71} - 42q^{72} - 353q^{73} + 750q^{74} + 95q^{75} - 19q^{76} + 165q^{78} - 34q^{79} - 852q^{80} - 671q^{81} + 720q^{82} - 234q^{83} + 1116q^{85} + 588q^{86} - 1245q^{87} - 1134q^{88} + 168q^{89} + 72q^{90} + 183q^{92} - 280q^{93} - 504q^{94} - 228q^{95} + 225q^{96} - 758q^{97} + 108q^{99} + O(q^{100}) \)

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
−3.00000 5.00000 1.00000 12.0000 −15.0000 0 21.0000 −2.00000 −36.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(19\) \(1\)

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 931.4.a.a 1
7.b odd 2 1 19.4.a.a 1
21.c even 2 1 171.4.a.d 1
28.d even 2 1 304.4.a.b 1
35.c odd 2 1 475.4.a.e 1
35.f even 4 2 475.4.b.c 2
56.e even 2 1 1216.4.a.a 1
56.h odd 2 1 1216.4.a.f 1
77.b even 2 1 2299.4.a.b 1
133.c even 2 1 361.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
19.4.a.a 1 7.b odd 2 1
171.4.a.d 1 21.c even 2 1
304.4.a.b 1 28.d even 2 1
361.4.a.b 1 133.c even 2 1
475.4.a.e 1 35.c odd 2 1
475.4.b.c 2 35.f even 4 2
931.4.a.a 1 1.a even 1 1 trivial
1216.4.a.a 1 56.e even 2 1
1216.4.a.f 1 56.h odd 2 1
2299.4.a.b 1 77.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(931))\):

\( T_{2} + 3 \)
\( T_{3} - 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 3 + T \)
$3$ \( -5 + T \)
$5$ \( -12 + T \)
$7$ \( T \)
$11$ \( 54 + T \)
$13$ \( 11 + T \)
$17$ \( -93 + T \)
$19$ \( 19 + T \)
$23$ \( -183 + T \)
$29$ \( 249 + T \)
$31$ \( 56 + T \)
$37$ \( 250 + T \)
$41$ \( 240 + T \)
$43$ \( 196 + T \)
$47$ \( -168 + T \)
$53$ \( -435 + T \)
$59$ \( 195 + T \)
$61$ \( -358 + T \)
$67$ \( 961 + T \)
$71$ \( 246 + T \)
$73$ \( 353 + T \)
$79$ \( 34 + T \)
$83$ \( 234 + T \)
$89$ \( -168 + T \)
$97$ \( 758 + T \)
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