Properties

Label 114.2.a.b
Level 114
Weight 2
Character orbit 114.a
Self dual yes
Analytic conductor 0.910
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 114.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.910294583043\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} + 2q^{13} - 2q^{15} + q^{16} - 6q^{17} + q^{18} - q^{19} + 2q^{20} - 4q^{22} - 4q^{23} - q^{24} - q^{25} + 2q^{26} - q^{27} - 2q^{29} - 2q^{30} + 4q^{31} + q^{32} + 4q^{33} - 6q^{34} + q^{36} + 10q^{37} - q^{38} - 2q^{39} + 2q^{40} + 10q^{41} + 4q^{43} - 4q^{44} + 2q^{45} - 4q^{46} - 4q^{47} - q^{48} - 7q^{49} - q^{50} + 6q^{51} + 2q^{52} - 10q^{53} - q^{54} - 8q^{55} + q^{57} - 2q^{58} + 12q^{59} - 2q^{60} + 14q^{61} + 4q^{62} + q^{64} + 4q^{65} + 4q^{66} - 12q^{67} - 6q^{68} + 4q^{69} + 8q^{71} + q^{72} - 6q^{73} + 10q^{74} + q^{75} - q^{76} - 2q^{78} - 4q^{79} + 2q^{80} + q^{81} + 10q^{82} + 12q^{83} - 12q^{85} + 4q^{86} + 2q^{87} - 4q^{88} - 6q^{89} + 2q^{90} - 4q^{92} - 4q^{93} - 4q^{94} - 2q^{95} - q^{96} + 10q^{97} - 7q^{98} - 4q^{99} + O(q^{100}) \)

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

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 114.2.a.b 1
3.b odd 2 1 342.2.a.b 1
4.b odd 2 1 912.2.a.k 1
5.b even 2 1 2850.2.a.j 1
5.c odd 4 2 2850.2.d.b 2
7.b odd 2 1 5586.2.a.y 1
8.b even 2 1 3648.2.a.x 1
8.d odd 2 1 3648.2.a.c 1
12.b even 2 1 2736.2.a.d 1
15.d odd 2 1 8550.2.a.ba 1
19.b odd 2 1 2166.2.a.d 1
57.d even 2 1 6498.2.a.p 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.2.a.b 1 1.a even 1 1 trivial
342.2.a.b 1 3.b odd 2 1
912.2.a.k 1 4.b odd 2 1
2166.2.a.d 1 19.b odd 2 1
2736.2.a.d 1 12.b even 2 1
2850.2.a.j 1 5.b even 2 1
2850.2.d.b 2 5.c odd 4 2
3648.2.a.c 1 8.d odd 2 1
3648.2.a.x 1 8.b even 2 1
5586.2.a.y 1 7.b odd 2 1
6498.2.a.p 1 57.d even 2 1
8550.2.a.ba 1 15.d odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(19\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(114))\):

\( T_{5} - 2 \)
\( T_{7} \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 + T \)
$5$ \( 1 - 2 T + 5 T^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 + 4 T + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + 6 T + 17 T^{2} \)
$19$ \( 1 + T \)
$23$ \( 1 + 4 T + 23 T^{2} \)
$29$ \( 1 + 2 T + 29 T^{2} \)
$31$ \( 1 - 4 T + 31 T^{2} \)
$37$ \( 1 - 10 T + 37 T^{2} \)
$41$ \( 1 - 10 T + 41 T^{2} \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 4 T + 47 T^{2} \)
$53$ \( 1 + 10 T + 53 T^{2} \)
$59$ \( 1 - 12 T + 59 T^{2} \)
$61$ \( 1 - 14 T + 61 T^{2} \)
$67$ \( 1 + 12 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 + 4 T + 79 T^{2} \)
$83$ \( 1 - 12 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 10 T + 97 T^{2} \)
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