Properties

Label 14.4.a.b
Level 14
Weight 4
Character orbit 14.a
Self dual yes
Analytic conductor 0.826
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.826026740080\)
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

\(f(q)\) \(=\) \( q + 2q^{2} - 2q^{3} + 4q^{4} - 12q^{5} - 4q^{6} + 7q^{7} + 8q^{8} - 23q^{9} + O(q^{10}) \) \( q + 2q^{2} - 2q^{3} + 4q^{4} - 12q^{5} - 4q^{6} + 7q^{7} + 8q^{8} - 23q^{9} - 24q^{10} + 48q^{11} - 8q^{12} + 56q^{13} + 14q^{14} + 24q^{15} + 16q^{16} - 114q^{17} - 46q^{18} + 2q^{19} - 48q^{20} - 14q^{21} + 96q^{22} - 120q^{23} - 16q^{24} + 19q^{25} + 112q^{26} + 100q^{27} + 28q^{28} - 54q^{29} + 48q^{30} + 236q^{31} + 32q^{32} - 96q^{33} - 228q^{34} - 84q^{35} - 92q^{36} + 146q^{37} + 4q^{38} - 112q^{39} - 96q^{40} + 126q^{41} - 28q^{42} - 376q^{43} + 192q^{44} + 276q^{45} - 240q^{46} - 12q^{47} - 32q^{48} + 49q^{49} + 38q^{50} + 228q^{51} + 224q^{52} + 174q^{53} + 200q^{54} - 576q^{55} + 56q^{56} - 4q^{57} - 108q^{58} + 138q^{59} + 96q^{60} + 380q^{61} + 472q^{62} - 161q^{63} + 64q^{64} - 672q^{65} - 192q^{66} - 484q^{67} - 456q^{68} + 240q^{69} - 168q^{70} + 576q^{71} - 184q^{72} - 1150q^{73} + 292q^{74} - 38q^{75} + 8q^{76} + 336q^{77} - 224q^{78} + 776q^{79} - 192q^{80} + 421q^{81} + 252q^{82} + 378q^{83} - 56q^{84} + 1368q^{85} - 752q^{86} + 108q^{87} + 384q^{88} - 390q^{89} + 552q^{90} + 392q^{91} - 480q^{92} - 472q^{93} - 24q^{94} - 24q^{95} - 64q^{96} - 1330q^{97} + 98q^{98} - 1104q^{99} + O(q^{100}) \)

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 −2.00000 4.00000 −12.0000 −4.00000 7.00000 8.00000 −23.0000 −24.0000
\(n\): 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 14.4.a.b 1
3.b odd 2 1 126.4.a.d 1
4.b odd 2 1 112.4.a.e 1
5.b even 2 1 350.4.a.f 1
5.c odd 4 2 350.4.c.g 2
7.b odd 2 1 98.4.a.e 1
7.c even 3 2 98.4.c.c 2
7.d odd 6 2 98.4.c.b 2
8.b even 2 1 448.4.a.k 1
8.d odd 2 1 448.4.a.g 1
11.b odd 2 1 1694.4.a.b 1
12.b even 2 1 1008.4.a.r 1
13.b even 2 1 2366.4.a.c 1
21.c even 2 1 882.4.a.b 1
21.g even 6 2 882.4.g.v 2
21.h odd 6 2 882.4.g.p 2
28.d even 2 1 784.4.a.h 1
35.c odd 2 1 2450.4.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.a.b 1 1.a even 1 1 trivial
98.4.a.e 1 7.b odd 2 1
98.4.c.b 2 7.d odd 6 2
98.4.c.c 2 7.c even 3 2
112.4.a.e 1 4.b odd 2 1
126.4.a.d 1 3.b odd 2 1
350.4.a.f 1 5.b even 2 1
350.4.c.g 2 5.c odd 4 2
448.4.a.g 1 8.d odd 2 1
448.4.a.k 1 8.b even 2 1
784.4.a.h 1 28.d even 2 1
882.4.a.b 1 21.c even 2 1
882.4.g.p 2 21.h odd 6 2
882.4.g.v 2 21.g even 6 2
1008.4.a.r 1 12.b even 2 1
1694.4.a.b 1 11.b odd 2 1
2366.4.a.c 1 13.b even 2 1
2450.4.a.i 1 35.c odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 2 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T \)
$3$ \( 1 + 2 T + 27 T^{2} \)
$5$ \( 1 + 12 T + 125 T^{2} \)
$7$ \( 1 - 7 T \)
$11$ \( 1 - 48 T + 1331 T^{2} \)
$13$ \( 1 - 56 T + 2197 T^{2} \)
$17$ \( 1 + 114 T + 4913 T^{2} \)
$19$ \( 1 - 2 T + 6859 T^{2} \)
$23$ \( 1 + 120 T + 12167 T^{2} \)
$29$ \( 1 + 54 T + 24389 T^{2} \)
$31$ \( 1 - 236 T + 29791 T^{2} \)
$37$ \( 1 - 146 T + 50653 T^{2} \)
$41$ \( 1 - 126 T + 68921 T^{2} \)
$43$ \( 1 + 376 T + 79507 T^{2} \)
$47$ \( 1 + 12 T + 103823 T^{2} \)
$53$ \( 1 - 174 T + 148877 T^{2} \)
$59$ \( 1 - 138 T + 205379 T^{2} \)
$61$ \( 1 - 380 T + 226981 T^{2} \)
$67$ \( 1 + 484 T + 300763 T^{2} \)
$71$ \( 1 - 576 T + 357911 T^{2} \)
$73$ \( 1 + 1150 T + 389017 T^{2} \)
$79$ \( 1 - 776 T + 493039 T^{2} \)
$83$ \( 1 - 378 T + 571787 T^{2} \)
$89$ \( 1 + 390 T + 704969 T^{2} \)
$97$ \( 1 + 1330 T + 912673 T^{2} \)
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