Properties

Label 6013.2.a.b
Level $6013$
Weight $2$
Character orbit 6013.a
Self dual yes
Analytic conductor $48.014$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 6013 = 7 \cdot 859 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6013.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - q^{3} + 2q^{4} - 2q^{6} - q^{7} - 2q^{9} + O(q^{10}) \) \( q + 2q^{2} - q^{3} + 2q^{4} - 2q^{6} - q^{7} - 2q^{9} - 2q^{12} + 6q^{13} - 2q^{14} - 4q^{16} - 4q^{18} + 4q^{19} + q^{21} - 2q^{23} - 5q^{25} + 12q^{26} + 5q^{27} - 2q^{28} + 8q^{29} - 10q^{31} - 8q^{32} - 4q^{36} + 8q^{38} - 6q^{39} + 2q^{41} + 2q^{42} + q^{43} - 4q^{46} + 12q^{47} + 4q^{48} + q^{49} - 10q^{50} + 12q^{52} + 3q^{53} + 10q^{54} - 4q^{57} + 16q^{58} - 8q^{59} + 10q^{61} - 20q^{62} + 2q^{63} - 8q^{64} - 2q^{67} + 2q^{69} + 8q^{71} - 9q^{73} + 5q^{75} + 8q^{76} - 12q^{78} + 15q^{79} + q^{81} + 4q^{82} + 15q^{83} + 2q^{84} + 2q^{86} - 8q^{87} - 7q^{89} - 6q^{91} - 4q^{92} + 10q^{93} + 24q^{94} + 8q^{96} + q^{97} + 2q^{98} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(859\) \(-1\)

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 6013.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6013.2.a.b 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6013))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( -6 + T \)
$17$ \( T \)
$19$ \( -4 + T \)
$23$ \( 2 + T \)
$29$ \( -8 + T \)
$31$ \( 10 + T \)
$37$ \( T \)
$41$ \( -2 + T \)
$43$ \( -1 + T \)
$47$ \( -12 + T \)
$53$ \( -3 + T \)
$59$ \( 8 + T \)
$61$ \( -10 + T \)
$67$ \( 2 + T \)
$71$ \( -8 + T \)
$73$ \( 9 + T \)
$79$ \( -15 + T \)
$83$ \( -15 + T \)
$89$ \( 7 + T \)
$97$ \( -1 + T \)
show more
show less