Properties

Label 196.4.a.c
Level $196$
Weight $4$
Character orbit 196.a
Self dual yes
Analytic conductor $11.564$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 196.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5643743611\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 4q^{3} + 20q^{5} - 11q^{9} + O(q^{10}) \) \( q + 4q^{3} + 20q^{5} - 11q^{9} + 44q^{11} + 44q^{13} + 80q^{15} - 72q^{17} - 100q^{19} - 120q^{23} + 275q^{25} - 152q^{27} + 218q^{29} + 280q^{31} + 176q^{33} - 30q^{37} + 176q^{39} - 120q^{41} + 220q^{43} - 220q^{45} - 88q^{47} - 288q^{51} + 110q^{53} + 880q^{55} - 400q^{57} - 580q^{59} - 380q^{61} + 880q^{65} - 980q^{67} - 480q^{69} - 112q^{71} + 640q^{73} + 1100q^{75} - 488q^{79} - 311q^{81} - 660q^{83} - 1440q^{85} + 872q^{87} - 320q^{89} + 1120q^{93} - 2000q^{95} - 248q^{97} - 484q^{99} + O(q^{100}) \)

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 4.00000 0 20.0000 0 0 0 −11.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 196.4.a.c yes 1
3.b odd 2 1 1764.4.a.a 1
4.b odd 2 1 784.4.a.f 1
7.b odd 2 1 196.4.a.a 1
7.c even 3 2 196.4.e.b 2
7.d odd 6 2 196.4.e.e 2
21.c even 2 1 1764.4.a.m 1
21.g even 6 2 1764.4.k.a 2
21.h odd 6 2 1764.4.k.p 2
28.d even 2 1 784.4.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
196.4.a.a 1 7.b odd 2 1
196.4.a.c yes 1 1.a even 1 1 trivial
196.4.e.b 2 7.c even 3 2
196.4.e.e 2 7.d odd 6 2
784.4.a.f 1 4.b odd 2 1
784.4.a.m 1 28.d even 2 1
1764.4.a.a 1 3.b odd 2 1
1764.4.a.m 1 21.c even 2 1
1764.4.k.a 2 21.g even 6 2
1764.4.k.p 2 21.h odd 6 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(196))\):

\( T_{3} - 4 \)
\( T_{5} - 20 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -4 + T \)
$5$ \( -20 + T \)
$7$ \( T \)
$11$ \( -44 + T \)
$13$ \( -44 + T \)
$17$ \( 72 + T \)
$19$ \( 100 + T \)
$23$ \( 120 + T \)
$29$ \( -218 + T \)
$31$ \( -280 + T \)
$37$ \( 30 + T \)
$41$ \( 120 + T \)
$43$ \( -220 + T \)
$47$ \( 88 + T \)
$53$ \( -110 + T \)
$59$ \( 580 + T \)
$61$ \( 380 + T \)
$67$ \( 980 + T \)
$71$ \( 112 + T \)
$73$ \( -640 + T \)
$79$ \( 488 + T \)
$83$ \( 660 + T \)
$89$ \( 320 + T \)
$97$ \( 248 + T \)
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