Properties

Label 14.4.a.a
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

\(f(q)\) \(=\) \( q - 2q^{2} + 8q^{3} + 4q^{4} - 14q^{5} - 16q^{6} - 7q^{7} - 8q^{8} + 37q^{9} + O(q^{10}) \) \( q - 2q^{2} + 8q^{3} + 4q^{4} - 14q^{5} - 16q^{6} - 7q^{7} - 8q^{8} + 37q^{9} + 28q^{10} - 28q^{11} + 32q^{12} + 18q^{13} + 14q^{14} - 112q^{15} + 16q^{16} + 74q^{17} - 74q^{18} + 80q^{19} - 56q^{20} - 56q^{21} + 56q^{22} - 112q^{23} - 64q^{24} + 71q^{25} - 36q^{26} + 80q^{27} - 28q^{28} + 190q^{29} + 224q^{30} + 72q^{31} - 32q^{32} - 224q^{33} - 148q^{34} + 98q^{35} + 148q^{36} - 346q^{37} - 160q^{38} + 144q^{39} + 112q^{40} + 162q^{41} + 112q^{42} - 412q^{43} - 112q^{44} - 518q^{45} + 224q^{46} + 24q^{47} + 128q^{48} + 49q^{49} - 142q^{50} + 592q^{51} + 72q^{52} + 318q^{53} - 160q^{54} + 392q^{55} + 56q^{56} + 640q^{57} - 380q^{58} - 200q^{59} - 448q^{60} - 198q^{61} - 144q^{62} - 259q^{63} + 64q^{64} - 252q^{65} + 448q^{66} - 716q^{67} + 296q^{68} - 896q^{69} - 196q^{70} + 392q^{71} - 296q^{72} + 538q^{73} + 692q^{74} + 568q^{75} + 320q^{76} + 196q^{77} - 288q^{78} + 240q^{79} - 224q^{80} - 359q^{81} - 324q^{82} - 1072q^{83} - 224q^{84} - 1036q^{85} + 824q^{86} + 1520q^{87} + 224q^{88} + 810q^{89} + 1036q^{90} - 126q^{91} - 448q^{92} + 576q^{93} - 48q^{94} - 1120q^{95} - 256q^{96} + 1354q^{97} - 98q^{98} - 1036q^{99} + O(q^{100}) \)

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 8.00000 4.00000 −14.0000 −16.0000 −7.00000 −8.00000 37.0000 28.0000
\(n\): 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.a 1
3.b odd 2 1 126.4.a.h 1
4.b odd 2 1 112.4.a.a 1
5.b even 2 1 350.4.a.l 1
5.c odd 4 2 350.4.c.b 2
7.b odd 2 1 98.4.a.a 1
7.c even 3 2 98.4.c.d 2
7.d odd 6 2 98.4.c.f 2
8.b even 2 1 448.4.a.b 1
8.d odd 2 1 448.4.a.o 1
11.b odd 2 1 1694.4.a.g 1
12.b even 2 1 1008.4.a.s 1
13.b even 2 1 2366.4.a.h 1
21.c even 2 1 882.4.a.i 1
21.g even 6 2 882.4.g.k 2
21.h odd 6 2 882.4.g.b 2
28.d even 2 1 784.4.a.s 1
35.c odd 2 1 2450.4.a.bo 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.a.a 1 1.a even 1 1 trivial
98.4.a.a 1 7.b odd 2 1
98.4.c.d 2 7.c even 3 2
98.4.c.f 2 7.d odd 6 2
112.4.a.a 1 4.b odd 2 1
126.4.a.h 1 3.b odd 2 1
350.4.a.l 1 5.b even 2 1
350.4.c.b 2 5.c odd 4 2
448.4.a.b 1 8.b even 2 1
448.4.a.o 1 8.d odd 2 1
784.4.a.s 1 28.d even 2 1
882.4.a.i 1 21.c even 2 1
882.4.g.b 2 21.h odd 6 2
882.4.g.k 2 21.g even 6 2
1008.4.a.s 1 12.b even 2 1
1694.4.a.g 1 11.b odd 2 1
2366.4.a.h 1 13.b even 2 1
2450.4.a.bo 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 \( T_{3} - 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T \)
$3$ \( 1 - 8 T + 27 T^{2} \)
$5$ \( 1 + 14 T + 125 T^{2} \)
$7$ \( 1 + 7 T \)
$11$ \( 1 + 28 T + 1331 T^{2} \)
$13$ \( 1 - 18 T + 2197 T^{2} \)
$17$ \( 1 - 74 T + 4913 T^{2} \)
$19$ \( 1 - 80 T + 6859 T^{2} \)
$23$ \( 1 + 112 T + 12167 T^{2} \)
$29$ \( 1 - 190 T + 24389 T^{2} \)
$31$ \( 1 - 72 T + 29791 T^{2} \)
$37$ \( 1 + 346 T + 50653 T^{2} \)
$41$ \( 1 - 162 T + 68921 T^{2} \)
$43$ \( 1 + 412 T + 79507 T^{2} \)
$47$ \( 1 - 24 T + 103823 T^{2} \)
$53$ \( 1 - 318 T + 148877 T^{2} \)
$59$ \( 1 + 200 T + 205379 T^{2} \)
$61$ \( 1 + 198 T + 226981 T^{2} \)
$67$ \( 1 + 716 T + 300763 T^{2} \)
$71$ \( 1 - 392 T + 357911 T^{2} \)
$73$ \( 1 - 538 T + 389017 T^{2} \)
$79$ \( 1 - 240 T + 493039 T^{2} \)
$83$ \( 1 + 1072 T + 571787 T^{2} \)
$89$ \( 1 - 810 T + 704969 T^{2} \)
$97$ \( 1 - 1354 T + 912673 T^{2} \)
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