Properties

Label 4900.2.a.i
Level $4900$
Weight $2$
Character orbit 4900.a
Self dual yes
Analytic conductor $39.127$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{3} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} - 2 q^{9} + 6 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} - 3 q^{23} + 5 q^{27} + 3 q^{29} + 2 q^{31} - 6 q^{33} - 8 q^{37} + 2 q^{39} - 3 q^{41} - 5 q^{43} - 6 q^{51} - 12 q^{53} - 8 q^{57} - q^{61} + 7 q^{67} + 3 q^{69} + 10 q^{73} - 4 q^{79} + q^{81} - 3 q^{83} - 3 q^{87} - 3 q^{89} - 2 q^{93} + 10 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −1.00000 0 0 0 0 0 −2.00000 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.i 1
5.b even 2 1 980.2.a.g 1
5.c odd 4 2 4900.2.e.m 2
7.b odd 2 1 4900.2.a.q 1
7.c even 3 2 700.2.i.b 2
15.d odd 2 1 8820.2.a.p 1
20.d odd 2 1 3920.2.a.k 1
35.c odd 2 1 980.2.a.e 1
35.f even 4 2 4900.2.e.n 2
35.i odd 6 2 980.2.i.f 2
35.j even 6 2 140.2.i.a 2
35.l odd 12 4 700.2.r.a 4
105.g even 2 1 8820.2.a.a 1
105.o odd 6 2 1260.2.s.c 2
140.c even 2 1 3920.2.a.w 1
140.p odd 6 2 560.2.q.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
140.2.i.a 2 35.j even 6 2
560.2.q.f 2 140.p odd 6 2
700.2.i.b 2 7.c even 3 2
700.2.r.a 4 35.l odd 12 4
980.2.a.e 1 35.c odd 2 1
980.2.a.g 1 5.b even 2 1
980.2.i.f 2 35.i odd 6 2
1260.2.s.c 2 105.o odd 6 2
3920.2.a.k 1 20.d odd 2 1
3920.2.a.w 1 140.c even 2 1
4900.2.a.i 1 1.a even 1 1 trivial
4900.2.a.q 1 7.b odd 2 1
4900.2.e.m 2 5.c odd 4 2
4900.2.e.n 2 35.f even 4 2
8820.2.a.a 1 105.g even 2 1
8820.2.a.p 1 15.d odd 2 1

Hecke kernels

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

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{11} - 6 \) Copy content Toggle raw display
\( T_{13} + 2 \) Copy content Toggle raw display
\( T_{19} - 8 \) Copy content Toggle raw display
\( T_{23} + 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

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