Properties

Label 4928.2.a.w
Level $4928$
Weight $2$
Character orbit 4928.a
Self dual yes
Analytic conductor $39.350$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 4q^{5} + q^{7} - 3q^{9} + O(q^{10}) \) \( q + 4q^{5} + q^{7} - 3q^{9} - q^{11} - 2q^{13} - 4q^{17} - 6q^{19} - 4q^{23} + 11q^{25} + 2q^{29} + 2q^{31} + 4q^{35} - 10q^{37} + 4q^{41} - 8q^{43} - 12q^{45} - 2q^{47} + q^{49} - 6q^{53} - 4q^{55} - 12q^{59} + 14q^{61} - 3q^{63} - 8q^{65} - 12q^{67} + 8q^{71} + 4q^{73} - q^{77} + 9q^{81} - 6q^{83} - 16q^{85} - 6q^{89} - 2q^{91} - 24q^{95} - 14q^{97} + 3q^{99} + O(q^{100}) \)

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 0 0 4.00000 0 1.00000 0 −3.00000 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.w 1
4.b odd 2 1 4928.2.a.v 1
8.b even 2 1 1232.2.a.e 1
8.d odd 2 1 154.2.a.a 1
24.f even 2 1 1386.2.a.l 1
40.e odd 2 1 3850.2.a.u 1
40.k even 4 2 3850.2.c.j 2
56.e even 2 1 1078.2.a.d 1
56.h odd 2 1 8624.2.a.r 1
56.k odd 6 2 1078.2.e.j 2
56.m even 6 2 1078.2.e.i 2
88.g even 2 1 1694.2.a.g 1
168.e odd 2 1 9702.2.a.ba 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.a 1 8.d odd 2 1
1078.2.a.d 1 56.e even 2 1
1078.2.e.i 2 56.m even 6 2
1078.2.e.j 2 56.k odd 6 2
1232.2.a.e 1 8.b even 2 1
1386.2.a.l 1 24.f even 2 1
1694.2.a.g 1 88.g even 2 1
3850.2.a.u 1 40.e odd 2 1
3850.2.c.j 2 40.k even 4 2
4928.2.a.v 1 4.b odd 2 1
4928.2.a.w 1 1.a even 1 1 trivial
8624.2.a.r 1 56.h odd 2 1
9702.2.a.ba 1 168.e odd 2 1

Hecke kernels

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( -4 + T \)
$7$ \( -1 + T \)
$11$ \( 1 + T \)
$13$ \( 2 + T \)
$17$ \( 4 + T \)
$19$ \( 6 + T \)
$23$ \( 4 + T \)
$29$ \( -2 + T \)
$31$ \( -2 + T \)
$37$ \( 10 + T \)
$41$ \( -4 + T \)
$43$ \( 8 + T \)
$47$ \( 2 + T \)
$53$ \( 6 + T \)
$59$ \( 12 + T \)
$61$ \( -14 + T \)
$67$ \( 12 + T \)
$71$ \( -8 + T \)
$73$ \( -4 + T \)
$79$ \( T \)
$83$ \( 6 + T \)
$89$ \( 6 + T \)
$97$ \( 14 + T \)
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