Properties

Label 4900.2.a.k
Level $4900$
Weight $2$
Character orbit 4900.a
Self dual yes
Analytic conductor $39.127$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.1266969904\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 700)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 3q^{9} + O(q^{10}) \) \( q - 3q^{9} - 5q^{11} + 6q^{13} - 4q^{17} + 6q^{19} + 3q^{23} - 3q^{29} - 2q^{31} + 7q^{37} + 4q^{41} - 7q^{43} + 2q^{47} - 10q^{53} + 14q^{59} - 4q^{61} + 3q^{67} - 13q^{71} - 16q^{73} + q^{79} + 9q^{81} - 10q^{83} - 10q^{89} + 2q^{97} + 15q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

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 4900.2.a.k 1
5.b even 2 1 4900.2.a.j 1
5.c odd 4 2 4900.2.e.o 2
7.b odd 2 1 700.2.a.g yes 1
21.c even 2 1 6300.2.a.be 1
28.d even 2 1 2800.2.a.q 1
35.c odd 2 1 700.2.a.e 1
35.f even 4 2 700.2.e.d 2
105.g even 2 1 6300.2.a.o 1
105.k odd 4 2 6300.2.k.q 2
140.c even 2 1 2800.2.a.t 1
140.j odd 4 2 2800.2.g.q 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
700.2.a.e 1 35.c odd 2 1
700.2.a.g yes 1 7.b odd 2 1
700.2.e.d 2 35.f even 4 2
2800.2.a.q 1 28.d even 2 1
2800.2.a.t 1 140.c even 2 1
2800.2.g.q 2 140.j odd 4 2
4900.2.a.j 1 5.b even 2 1
4900.2.a.k 1 1.a even 1 1 trivial
4900.2.e.o 2 5.c odd 4 2
6300.2.a.o 1 105.g even 2 1
6300.2.a.be 1 21.c even 2 1
6300.2.k.q 2 105.k odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4900))\):

\( T_{3} \)
\( T_{11} + 5 \)
\( T_{13} - 6 \)
\( T_{19} - 6 \)
\( T_{23} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( 5 + T \)
$13$ \( -6 + T \)
$17$ \( 4 + T \)
$19$ \( -6 + T \)
$23$ \( -3 + T \)
$29$ \( 3 + T \)
$31$ \( 2 + T \)
$37$ \( -7 + T \)
$41$ \( -4 + T \)
$43$ \( 7 + T \)
$47$ \( -2 + T \)
$53$ \( 10 + T \)
$59$ \( -14 + T \)
$61$ \( 4 + T \)
$67$ \( -3 + T \)
$71$ \( 13 + T \)
$73$ \( 16 + T \)
$79$ \( -1 + T \)
$83$ \( 10 + T \)
$89$ \( 10 + T \)
$97$ \( -2 + T \)
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