Properties

Label 2420.2.a.e
Level 2420
Weight 2
Character orbit 2420.a
Self dual yes
Analytic conductor 19.324
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2420.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.3237972891\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + q^{3} - q^{5} - q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - q^{5} - q^{7} - 2q^{9} + 2q^{13} - q^{15} + 2q^{19} - q^{21} + q^{25} - 5q^{27} - 6q^{29} - 4q^{31} + q^{35} - 4q^{37} + 2q^{39} + 9q^{41} - q^{43} + 2q^{45} - 3q^{47} - 6q^{49} - 6q^{53} + 2q^{57} - q^{61} + 2q^{63} - 2q^{65} - 13q^{67} - 12q^{71} - 16q^{73} + q^{75} - 10q^{79} + q^{81} + 12q^{83} - 6q^{87} - 3q^{89} - 2q^{91} - 4q^{93} - 2q^{95} - 10q^{97} + O(q^{100}) \)

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 1.00000 0 −1.00000 0 −1.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 2420.2.a.e 1
4.b odd 2 1 9680.2.a.h 1
11.b odd 2 1 2420.2.a.f yes 1
44.c even 2 1 9680.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2420.2.a.e 1 1.a even 1 1 trivial
2420.2.a.f yes 1 11.b odd 2 1
9680.2.a.f 1 44.c even 2 1
9680.2.a.h 1 4.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(11\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\):

\( T_{3} - 1 \)
\( T_{7} + 1 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 - T + 3 T^{2} \)
$5$ \( 1 + T \)
$7$ \( 1 + T + 7 T^{2} \)
$11$ \( \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + 17 T^{2} \)
$19$ \( 1 - 2 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 + 4 T + 37 T^{2} \)
$41$ \( 1 - 9 T + 41 T^{2} \)
$43$ \( 1 + T + 43 T^{2} \)
$47$ \( 1 + 3 T + 47 T^{2} \)
$53$ \( 1 + 6 T + 53 T^{2} \)
$59$ \( 1 + 59 T^{2} \)
$61$ \( 1 + T + 61 T^{2} \)
$67$ \( 1 + 13 T + 67 T^{2} \)
$71$ \( 1 + 12 T + 71 T^{2} \)
$73$ \( 1 + 16 T + 73 T^{2} \)
$79$ \( 1 + 10 T + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 + 3 T + 89 T^{2} \)
$97$ \( 1 + 10 T + 97 T^{2} \)
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