Properties

Label 114.4.a.b
Level $114$
Weight $4$
Character orbit 114.a
Self dual yes
Analytic conductor $6.726$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.72621774065\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 2q^{2} + 3q^{3} + 4q^{4} - 7q^{5} - 6q^{6} - 15q^{7} - 8q^{8} + 9q^{9} + O(q^{10}) \) \( q - 2q^{2} + 3q^{3} + 4q^{4} - 7q^{5} - 6q^{6} - 15q^{7} - 8q^{8} + 9q^{9} + 14q^{10} - 49q^{11} + 12q^{12} + 14q^{13} + 30q^{14} - 21q^{15} + 16q^{16} - 33q^{17} - 18q^{18} - 19q^{19} - 28q^{20} - 45q^{21} + 98q^{22} - 148q^{23} - 24q^{24} - 76q^{25} - 28q^{26} + 27q^{27} - 60q^{28} - 278q^{29} + 42q^{30} + 94q^{31} - 32q^{32} - 147q^{33} + 66q^{34} + 105q^{35} + 36q^{36} + 160q^{37} + 38q^{38} + 42q^{39} + 56q^{40} + 400q^{41} + 90q^{42} + 73q^{43} - 196q^{44} - 63q^{45} + 296q^{46} + 173q^{47} + 48q^{48} - 118q^{49} + 152q^{50} - 99q^{51} + 56q^{52} + 170q^{53} - 54q^{54} + 343q^{55} + 120q^{56} - 57q^{57} + 556q^{58} - 12q^{59} - 84q^{60} + 419q^{61} - 188q^{62} - 135q^{63} + 64q^{64} - 98q^{65} + 294q^{66} + 444q^{67} - 132q^{68} - 444q^{69} - 210q^{70} - 952q^{71} - 72q^{72} - 27q^{73} - 320q^{74} - 228q^{75} - 76q^{76} + 735q^{77} - 84q^{78} - 556q^{79} - 112q^{80} + 81q^{81} - 800q^{82} - 276q^{83} - 180q^{84} + 231q^{85} - 146q^{86} - 834q^{87} + 392q^{88} + 1386q^{89} + 126q^{90} - 210q^{91} - 592q^{92} + 282q^{93} - 346q^{94} + 133q^{95} - 96q^{96} + 130q^{97} + 236q^{98} - 441q^{99} + O(q^{100}) \)

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
−2.00000 3.00000 4.00000 −7.00000 −6.00000 −15.0000 −8.00000 9.00000 14.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 114.4.a.b 1
3.b odd 2 1 342.4.a.c 1
4.b odd 2 1 912.4.a.b 1
19.b odd 2 1 2166.4.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.4.a.b 1 1.a even 1 1 trivial
342.4.a.c 1 3.b odd 2 1
912.4.a.b 1 4.b odd 2 1
2166.4.a.d 1 19.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} + 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(114))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( -3 + T \)
$5$ \( 7 + T \)
$7$ \( 15 + T \)
$11$ \( 49 + T \)
$13$ \( -14 + T \)
$17$ \( 33 + T \)
$19$ \( 19 + T \)
$23$ \( 148 + T \)
$29$ \( 278 + T \)
$31$ \( -94 + T \)
$37$ \( -160 + T \)
$41$ \( -400 + T \)
$43$ \( -73 + T \)
$47$ \( -173 + T \)
$53$ \( -170 + T \)
$59$ \( 12 + T \)
$61$ \( -419 + T \)
$67$ \( -444 + T \)
$71$ \( 952 + T \)
$73$ \( 27 + T \)
$79$ \( 556 + T \)
$83$ \( 276 + T \)
$89$ \( -1386 + T \)
$97$ \( -130 + T \)
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