Properties

Label 14.10.a.a
Level 14
Weight 10
Character orbit 14.a
Self dual yes
Analytic conductor 7.211
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.21050170629\)
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

\(f(q)\) \(=\) \( q - 16q^{2} - 6q^{3} + 256q^{4} + 560q^{5} + 96q^{6} - 2401q^{7} - 4096q^{8} - 19647q^{9} + O(q^{10}) \) \( q - 16q^{2} - 6q^{3} + 256q^{4} + 560q^{5} + 96q^{6} - 2401q^{7} - 4096q^{8} - 19647q^{9} - 8960q^{10} - 54152q^{11} - 1536q^{12} - 113172q^{13} + 38416q^{14} - 3360q^{15} + 65536q^{16} + 6262q^{17} + 314352q^{18} + 257078q^{19} + 143360q^{20} + 14406q^{21} + 866432q^{22} - 266000q^{23} + 24576q^{24} - 1639525q^{25} + 1810752q^{26} + 235980q^{27} - 614656q^{28} + 1574714q^{29} + 53760q^{30} - 4637484q^{31} - 1048576q^{32} + 324912q^{33} - 100192q^{34} - 1344560q^{35} - 5029632q^{36} - 11946238q^{37} - 4113248q^{38} + 679032q^{39} - 2293760q^{40} + 21909126q^{41} - 230496q^{42} + 27520592q^{43} - 13862912q^{44} - 11002320q^{45} + 4256000q^{46} + 52927836q^{47} - 393216q^{48} + 5764801q^{49} + 26232400q^{50} - 37572q^{51} - 28972032q^{52} + 16221222q^{53} - 3775680q^{54} - 30325120q^{55} + 9834496q^{56} - 1542468q^{57} - 25195424q^{58} - 140509618q^{59} - 860160q^{60} - 202963560q^{61} + 74199744q^{62} + 47172447q^{63} + 16777216q^{64} - 63376320q^{65} - 5198592q^{66} + 153734572q^{67} + 1603072q^{68} + 1596000q^{69} + 21512960q^{70} + 279655936q^{71} + 80474112q^{72} - 404022830q^{73} + 191139808q^{74} + 9837150q^{75} + 65811968q^{76} + 130018952q^{77} - 10864512q^{78} - 130689816q^{79} + 36700160q^{80} + 385296021q^{81} - 350546016q^{82} + 420134014q^{83} + 3687936q^{84} + 3506720q^{85} - 440329472q^{86} - 9448284q^{87} + 221806592q^{88} - 469542390q^{89} + 176037120q^{90} + 271725972q^{91} - 68096000q^{92} + 27824904q^{93} - 846845376q^{94} + 143963680q^{95} + 6291456q^{96} - 872501690q^{97} - 92236816q^{98} + 1063924344q^{99} + O(q^{100}) \)

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
−16.0000 −6.00000 256.000 560.000 96.0000 −2401.00 −4096.00 −19647.0 −8960.00
\(n\): 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 14.10.a.a 1
3.b odd 2 1 126.10.a.e 1
4.b odd 2 1 112.10.a.b 1
5.b even 2 1 350.10.a.c 1
5.c odd 4 2 350.10.c.b 2
7.b odd 2 1 98.10.a.a 1
7.c even 3 2 98.10.c.f 2
7.d odd 6 2 98.10.c.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.10.a.a 1 1.a even 1 1 trivial
98.10.a.a 1 7.b odd 2 1
98.10.c.e 2 7.d odd 6 2
98.10.c.f 2 7.c even 3 2
112.10.a.b 1 4.b odd 2 1
126.10.a.e 1 3.b odd 2 1
350.10.a.c 1 5.b even 2 1
350.10.c.b 2 5.c odd 4 2

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 6 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 16 T \)
$3$ \( 1 + 6 T + 19683 T^{2} \)
$5$ \( 1 - 560 T + 1953125 T^{2} \)
$7$ \( 1 + 2401 T \)
$11$ \( 1 + 54152 T + 2357947691 T^{2} \)
$13$ \( 1 + 113172 T + 10604499373 T^{2} \)
$17$ \( 1 - 6262 T + 118587876497 T^{2} \)
$19$ \( 1 - 257078 T + 322687697779 T^{2} \)
$23$ \( 1 + 266000 T + 1801152661463 T^{2} \)
$29$ \( 1 - 1574714 T + 14507145975869 T^{2} \)
$31$ \( 1 + 4637484 T + 26439622160671 T^{2} \)
$37$ \( 1 + 11946238 T + 129961739795077 T^{2} \)
$41$ \( 1 - 21909126 T + 327381934393961 T^{2} \)
$43$ \( 1 - 27520592 T + 502592611936843 T^{2} \)
$47$ \( 1 - 52927836 T + 1119130473102767 T^{2} \)
$53$ \( 1 - 16221222 T + 3299763591802133 T^{2} \)
$59$ \( 1 + 140509618 T + 8662995818654939 T^{2} \)
$61$ \( 1 + 202963560 T + 11694146092834141 T^{2} \)
$67$ \( 1 - 153734572 T + 27206534396294947 T^{2} \)
$71$ \( 1 - 279655936 T + 45848500718449031 T^{2} \)
$73$ \( 1 + 404022830 T + 58871586708267913 T^{2} \)
$79$ \( 1 + 130689816 T + 119851595982618319 T^{2} \)
$83$ \( 1 - 420134014 T + 186940255267540403 T^{2} \)
$89$ \( 1 + 469542390 T + 350356403707485209 T^{2} \)
$97$ \( 1 + 872501690 T + 760231058654565217 T^{2} \)
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