Properties

Label 4140.2.a.d
Level $4140$
Weight $2$
Character orbit 4140.a
Self dual yes
Analytic conductor $33.058$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.0580664368\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 460)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{5} - 2 q^{7} + 4 q^{11} + q^{13} - 4 q^{19} + q^{23} + q^{25} + 7 q^{29} - 7 q^{31} + 2 q^{35} - 4 q^{37} - 3 q^{41} + 6 q^{43} + 13 q^{47} - 3 q^{49} - 10 q^{53} - 4 q^{55} + 8 q^{59} - q^{65} + 8 q^{67} - 13 q^{71} + 11 q^{73} - 8 q^{77} + 4 q^{79} + 4 q^{83} + 6 q^{89} - 2 q^{91} + 4 q^{95} - 2 q^{97}+O(q^{100}) \) 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 0 0 −1.00000 0 −2.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(23\) \(-1\)

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 4140.2.a.d 1
3.b odd 2 1 460.2.a.a 1
12.b even 2 1 1840.2.a.h 1
15.d odd 2 1 2300.2.a.f 1
15.e even 4 2 2300.2.c.e 2
24.f even 2 1 7360.2.a.h 1
24.h odd 2 1 7360.2.a.s 1
60.h even 2 1 9200.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.a.a 1 3.b odd 2 1
1840.2.a.h 1 12.b even 2 1
2300.2.a.f 1 15.d odd 2 1
2300.2.c.e 2 15.e even 4 2
4140.2.a.d 1 1.a even 1 1 trivial
7360.2.a.h 1 24.f even 2 1
7360.2.a.s 1 24.h odd 2 1
9200.2.a.m 1 60.h even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4140))\):

\( T_{7} + 2 \) Copy content Toggle raw display
\( T_{11} - 4 \) Copy content Toggle raw display
\( T_{13} - 1 \) Copy content Toggle raw display
\( T_{17} \) Copy content Toggle raw display

Hecke characteristic polynomials

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