Properties

Label 6014.2.a.a
Level $6014$
Weight $2$
Character orbit 6014.a
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0220317756\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + 3q^{5} - q^{6} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + 3q^{5} - q^{6} + q^{8} - 2q^{9} + 3q^{10} + q^{11} - q^{12} + 6q^{13} - 3q^{15} + q^{16} - q^{17} - 2q^{18} + 7q^{19} + 3q^{20} + q^{22} + 7q^{23} - q^{24} + 4q^{25} + 6q^{26} + 5q^{27} - 3q^{30} + q^{31} + q^{32} - q^{33} - q^{34} - 2q^{36} - 4q^{37} + 7q^{38} - 6q^{39} + 3q^{40} + 2q^{41} - 11q^{43} + q^{44} - 6q^{45} + 7q^{46} - 13q^{47} - q^{48} - 7q^{49} + 4q^{50} + q^{51} + 6q^{52} - q^{53} + 5q^{54} + 3q^{55} - 7q^{57} + 7q^{59} - 3q^{60} + 10q^{61} + q^{62} + q^{64} + 18q^{65} - q^{66} - 4q^{67} - q^{68} - 7q^{69} + 10q^{71} - 2q^{72} - 4q^{73} - 4q^{74} - 4q^{75} + 7q^{76} - 6q^{78} - 12q^{79} + 3q^{80} + q^{81} + 2q^{82} - 2q^{83} - 3q^{85} - 11q^{86} + q^{88} + 6q^{89} - 6q^{90} + 7q^{92} - q^{93} - 13q^{94} + 21q^{95} - q^{96} + q^{97} - 7q^{98} - 2q^{99} + O(q^{100}) \)

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
1.00000 −1.00000 1.00000 3.00000 −1.00000 0 1.00000 −2.00000 3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(31\) \(-1\)
\(97\) \(-1\)

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 6014.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6014.2.a.a 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).

Hecke characteristic polynomials

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