Properties

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

Related objects

Downloads

Learn more

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 140)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 3 q^{3} + 6 q^{9} + O(q^{10}) \) \( q - 3 q^{3} + 6 q^{9} - 2 q^{11} - 6 q^{13} + 2 q^{17} + 9 q^{23} - 9 q^{27} + 3 q^{29} - 2 q^{31} + 6 q^{33} - 8 q^{37} + 18 q^{39} - 5 q^{41} - q^{43} + 8 q^{47} - 6 q^{51} - 4 q^{53} + 8 q^{59} - 7 q^{61} + 3 q^{67} - 27 q^{69} + 8 q^{71} + 14 q^{73} + 4 q^{79} + 9 q^{81} - q^{83} - 9 q^{87} - 13 q^{89} + 6 q^{93} - 10 q^{97} - 12 q^{99} + O(q^{100}) \)

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 0 0 0 0 6.00000 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.a 1
5.b even 2 1 980.2.a.i 1
5.c odd 4 2 4900.2.e.b 2
7.b odd 2 1 4900.2.a.v 1
7.d odd 6 2 700.2.i.a 2
15.d odd 2 1 8820.2.a.k 1
20.d odd 2 1 3920.2.a.d 1
35.c odd 2 1 980.2.a.a 1
35.f even 4 2 4900.2.e.c 2
35.i odd 6 2 140.2.i.b 2
35.j even 6 2 980.2.i.a 2
35.k even 12 4 700.2.r.c 4
105.g even 2 1 8820.2.a.w 1
105.p even 6 2 1260.2.s.b 2
140.c even 2 1 3920.2.a.bi 1
140.s even 6 2 560.2.q.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
140.2.i.b 2 35.i odd 6 2
560.2.q.a 2 140.s even 6 2
700.2.i.a 2 7.d odd 6 2
700.2.r.c 4 35.k even 12 4
980.2.a.a 1 35.c odd 2 1
980.2.a.i 1 5.b even 2 1
980.2.i.a 2 35.j even 6 2
1260.2.s.b 2 105.p even 6 2
3920.2.a.d 1 20.d odd 2 1
3920.2.a.bi 1 140.c even 2 1
4900.2.a.a 1 1.a even 1 1 trivial
4900.2.a.v 1 7.b odd 2 1
4900.2.e.b 2 5.c odd 4 2
4900.2.e.c 2 35.f even 4 2
8820.2.a.k 1 15.d odd 2 1
8820.2.a.w 1 105.g even 2 1

Hecke kernels

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

\( T_{3} + 3 \)
\( T_{11} + 2 \)
\( T_{13} + 6 \)
\( T_{19} \)
\( T_{23} - 9 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 3 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( 2 + T \)
$13$ \( 6 + T \)
$17$ \( -2 + T \)
$19$ \( T \)
$23$ \( -9 + T \)
$29$ \( -3 + T \)
$31$ \( 2 + T \)
$37$ \( 8 + T \)
$41$ \( 5 + T \)
$43$ \( 1 + T \)
$47$ \( -8 + T \)
$53$ \( 4 + T \)
$59$ \( -8 + T \)
$61$ \( 7 + T \)
$67$ \( -3 + T \)
$71$ \( -8 + T \)
$73$ \( -14 + T \)
$79$ \( -4 + T \)
$83$ \( 1 + T \)
$89$ \( 13 + T \)
$97$ \( 10 + T \)
show more
show less