Properties

Label 4600.2.a.g
Level $4600$
Weight $2$
Character orbit 4600.a
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 184)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 4 q^{7} - 3 q^{9} + O(q^{10}) \) \( q - 4 q^{7} - 3 q^{9} + 6 q^{11} + 2 q^{13} - 6 q^{17} - 6 q^{19} - q^{23} - 6 q^{29} + 8 q^{37} + 6 q^{41} + 2 q^{43} + 8 q^{47} + 9 q^{49} + 8 q^{53} + 4 q^{59} - 4 q^{61} + 12 q^{63} - 2 q^{67} - 8 q^{71} - 6 q^{73} - 24 q^{77} + 12 q^{79} + 9 q^{81} - 10 q^{83} + 10 q^{89} - 8 q^{91} + 18 q^{97} - 18 q^{99} + O(q^{100}) \)

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 0 0 0 0 −4.00000 0 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 4600.2.a.g 1
4.b odd 2 1 9200.2.a.x 1
5.b even 2 1 184.2.a.c 1
5.c odd 4 2 4600.2.e.k 2
15.d odd 2 1 1656.2.a.e 1
20.d odd 2 1 368.2.a.c 1
35.c odd 2 1 9016.2.a.i 1
40.e odd 2 1 1472.2.a.h 1
40.f even 2 1 1472.2.a.i 1
60.h even 2 1 3312.2.a.f 1
115.c odd 2 1 4232.2.a.g 1
460.g even 2 1 8464.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.a.c 1 5.b even 2 1
368.2.a.c 1 20.d odd 2 1
1472.2.a.h 1 40.e odd 2 1
1472.2.a.i 1 40.f even 2 1
1656.2.a.e 1 15.d odd 2 1
3312.2.a.f 1 60.h even 2 1
4232.2.a.g 1 115.c odd 2 1
4600.2.a.g 1 1.a even 1 1 trivial
4600.2.e.k 2 5.c odd 4 2
8464.2.a.i 1 460.g even 2 1
9016.2.a.i 1 35.c odd 2 1
9200.2.a.x 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\):

\( T_{3} \)
\( T_{7} + 4 \)
\( T_{11} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 4 + T \)
$11$ \( -6 + T \)
$13$ \( -2 + T \)
$17$ \( 6 + T \)
$19$ \( 6 + T \)
$23$ \( 1 + T \)
$29$ \( 6 + T \)
$31$ \( T \)
$37$ \( -8 + T \)
$41$ \( -6 + T \)
$43$ \( -2 + T \)
$47$ \( -8 + T \)
$53$ \( -8 + T \)
$59$ \( -4 + T \)
$61$ \( 4 + T \)
$67$ \( 2 + T \)
$71$ \( 8 + T \)
$73$ \( 6 + T \)
$79$ \( -12 + T \)
$83$ \( 10 + T \)
$89$ \( -10 + T \)
$97$ \( -18 + T \)
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