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

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: Complex embeddings Normalized embeddings Satake parameters Satake angles

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 14.10.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

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

$p$ $F_p(T)$
$2$ $$16 + T$$
$3$ $$6 + T$$
$5$ $$-560 + T$$
$7$ $$2401 + T$$
$11$ $$54152 + T$$
$13$ $$113172 + T$$
$17$ $$-6262 + T$$
$19$ $$-257078 + T$$
$23$ $$266000 + T$$
$29$ $$-1574714 + T$$
$31$ $$4637484 + T$$
$37$ $$11946238 + T$$
$41$ $$-21909126 + T$$
$43$ $$-27520592 + T$$
$47$ $$-52927836 + T$$
$53$ $$-16221222 + T$$
$59$ $$140509618 + T$$
$61$ $$202963560 + T$$
$67$ $$-153734572 + T$$
$71$ $$-279655936 + T$$
$73$ $$404022830 + T$$
$79$ $$130689816 + T$$
$83$ $$-420134014 + T$$
$89$ $$469542390 + T$$
$97$ $$872501690 + T$$