Properties

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

Related objects

Downloads

Learn more

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

\(f(q)\) \(=\) \( q - 3q^{3} + 2q^{7} + 6q^{9} + O(q^{10}) \) \( q - 3q^{3} + 2q^{7} + 6q^{9} + 5q^{13} + 6q^{17} + 6q^{19} - 6q^{21} - q^{23} - 9q^{27} + 9q^{29} + 3q^{31} + 8q^{37} - 15q^{39} + 3q^{41} + 8q^{43} - 7q^{47} - 3q^{49} - 18q^{51} + 2q^{53} - 18q^{57} + 4q^{59} - 10q^{61} + 12q^{63} - 8q^{67} + 3q^{69} + 7q^{71} - 9q^{73} - 6q^{79} + 9q^{81} + 14q^{83} - 27q^{87} + 16q^{89} + 10q^{91} - 9q^{93} - 6q^{97} + O(q^{100}) \)

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 −3.00000 0 0 0 2.00000 0 6.00000 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.a 1
4.b odd 2 1 9200.2.a.bj 1
5.b even 2 1 184.2.a.d 1
5.c odd 4 2 4600.2.e.a 2
15.d odd 2 1 1656.2.a.c 1
20.d odd 2 1 368.2.a.a 1
35.c odd 2 1 9016.2.a.b 1
40.e odd 2 1 1472.2.a.m 1
40.f even 2 1 1472.2.a.a 1
60.h even 2 1 3312.2.a.i 1
115.c odd 2 1 4232.2.a.j 1
460.g even 2 1 8464.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.a.d 1 5.b even 2 1
368.2.a.a 1 20.d odd 2 1
1472.2.a.a 1 40.f even 2 1
1472.2.a.m 1 40.e odd 2 1
1656.2.a.c 1 15.d odd 2 1
3312.2.a.i 1 60.h even 2 1
4232.2.a.j 1 115.c odd 2 1
4600.2.a.a 1 1.a even 1 1 trivial
4600.2.e.a 2 5.c odd 4 2
8464.2.a.b 1 460.g even 2 1
9016.2.a.b 1 35.c odd 2 1
9200.2.a.bj 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\):

\( T_{3} + 3 \)
\( T_{7} - 2 \)
\( T_{11} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 3 + T \)
$5$ \( T \)
$7$ \( -2 + T \)
$11$ \( T \)
$13$ \( -5 + T \)
$17$ \( -6 + T \)
$19$ \( -6 + T \)
$23$ \( 1 + T \)
$29$ \( -9 + T \)
$31$ \( -3 + T \)
$37$ \( -8 + T \)
$41$ \( -3 + T \)
$43$ \( -8 + T \)
$47$ \( 7 + T \)
$53$ \( -2 + T \)
$59$ \( -4 + T \)
$61$ \( 10 + T \)
$67$ \( 8 + T \)
$71$ \( -7 + T \)
$73$ \( 9 + T \)
$79$ \( 6 + T \)
$83$ \( -14 + T \)
$89$ \( -16 + T \)
$97$ \( 6 + T \)
show more
show less