Properties

Label 4928.2.a.bj
Level $4928$
Weight $2$
Character orbit 4928.a
Self dual yes
Analytic conductor $39.350$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4928 = 2^{6} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4928.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.3502781161\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{3} + q^{5} - q^{7} + 6 q^{9} + O(q^{10}) \) \( q + 3 q^{3} + q^{5} - q^{7} + 6 q^{9} + q^{11} + 4 q^{13} + 3 q^{15} + 2 q^{17} + 6 q^{19} - 3 q^{21} - 5 q^{23} - 4 q^{25} + 9 q^{27} - 10 q^{29} + q^{31} + 3 q^{33} - q^{35} + 5 q^{37} + 12 q^{39} - 2 q^{41} + 8 q^{43} + 6 q^{45} + 8 q^{47} + q^{49} + 6 q^{51} + 6 q^{53} + q^{55} + 18 q^{57} - 3 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 3 q^{67} - 15 q^{69} + q^{71} + 10 q^{73} - 12 q^{75} - q^{77} + 6 q^{79} + 9 q^{81} - 12 q^{83} + 2 q^{85} - 30 q^{87} - 15 q^{89} - 4 q^{91} + 3 q^{93} + 6 q^{95} - 5 q^{97} + 6 q^{99} + O(q^{100}) \)

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
0 3.00000 0 1.00000 0 −1.00000 0 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)
\(11\) \(-1\)

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 4928.2.a.bj 1
4.b odd 2 1 4928.2.a.a 1
8.b even 2 1 77.2.a.a 1
8.d odd 2 1 1232.2.a.l 1
24.h odd 2 1 693.2.a.c 1
40.f even 2 1 1925.2.a.h 1
40.i odd 4 2 1925.2.b.e 2
56.e even 2 1 8624.2.a.a 1
56.h odd 2 1 539.2.a.c 1
56.j odd 6 2 539.2.e.c 2
56.p even 6 2 539.2.e.f 2
88.b odd 2 1 847.2.a.b 1
88.o even 10 4 847.2.f.i 4
88.p odd 10 4 847.2.f.h 4
168.i even 2 1 4851.2.a.j 1
264.m even 2 1 7623.2.a.j 1
616.o even 2 1 5929.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
77.2.a.a 1 8.b even 2 1
539.2.a.c 1 56.h odd 2 1
539.2.e.c 2 56.j odd 6 2
539.2.e.f 2 56.p even 6 2
693.2.a.c 1 24.h odd 2 1
847.2.a.b 1 88.b odd 2 1
847.2.f.h 4 88.p odd 10 4
847.2.f.i 4 88.o even 10 4
1232.2.a.l 1 8.d odd 2 1
1925.2.a.h 1 40.f even 2 1
1925.2.b.e 2 40.i odd 4 2
4851.2.a.j 1 168.i even 2 1
4928.2.a.a 1 4.b odd 2 1
4928.2.a.bj 1 1.a even 1 1 trivial
5929.2.a.f 1 616.o even 2 1
7623.2.a.j 1 264.m even 2 1
8624.2.a.a 1 56.e even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4928))\):

\( T_{3} - 3 \)
\( T_{5} - 1 \)
\( T_{13} - 4 \)
\( T_{17} - 2 \)
\( T_{19} - 6 \)
\( T_{23} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -3 + T \)
$5$ \( -1 + T \)
$7$ \( 1 + T \)
$11$ \( -1 + T \)
$13$ \( -4 + T \)
$17$ \( -2 + T \)
$19$ \( -6 + T \)
$23$ \( 5 + T \)
$29$ \( 10 + T \)
$31$ \( -1 + T \)
$37$ \( -5 + T \)
$41$ \( 2 + T \)
$43$ \( -8 + T \)
$47$ \( -8 + T \)
$53$ \( -6 + T \)
$59$ \( 3 + T \)
$61$ \( -2 + T \)
$67$ \( -3 + T \)
$71$ \( -1 + T \)
$73$ \( -10 + T \)
$79$ \( -6 + T \)
$83$ \( 12 + T \)
$89$ \( 15 + T \)
$97$ \( 5 + T \)
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