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

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

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:

Atkin-Lehner signs

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

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 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

Hecke kernels

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T + 2 \) Copy content Toggle raw display
$5$ \( T + 12 \) Copy content Toggle raw display
$7$ \( T - 7 \) Copy content Toggle raw display
$11$ \( T - 48 \) Copy content Toggle raw display
$13$ \( T - 56 \) Copy content Toggle raw display
$17$ \( T + 114 \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T + 120 \) Copy content Toggle raw display
$29$ \( T + 54 \) Copy content Toggle raw display
$31$ \( T - 236 \) Copy content Toggle raw display
$37$ \( T - 146 \) Copy content Toggle raw display
$41$ \( T - 126 \) Copy content Toggle raw display
$43$ \( T + 376 \) Copy content Toggle raw display
$47$ \( T + 12 \) Copy content Toggle raw display
$53$ \( T - 174 \) Copy content Toggle raw display
$59$ \( T - 138 \) Copy content Toggle raw display
$61$ \( T - 380 \) Copy content Toggle raw display
$67$ \( T + 484 \) Copy content Toggle raw display
$71$ \( T - 576 \) Copy content Toggle raw display
$73$ \( T + 1150 \) Copy content Toggle raw display
$79$ \( T - 776 \) Copy content Toggle raw display
$83$ \( T - 378 \) Copy content Toggle raw display
$89$ \( T + 390 \) Copy content Toggle raw display
$97$ \( T + 1330 \) Copy content Toggle raw display
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