LMFDB - Newform 14.4.c.a

Newspace parameters

Level:	$ N $	=	$ 14 = 2 \cdot 7 $
Weight:	$ k $	=	$ 4 $
Character orbit:	$[\chi]$	=	14.c (of order $3$ and degree $2$)

Newform invariants

Self dual:	No
Analytic conductor:	$0.82602674008$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-3}) $
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of a primitive root of unity $\zeta_{6}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	$ q$ $ + ( -2 + 2 \zeta_{6} ) q^{2} $ $ + 5 \zeta_{6} q^{3} $ $ -4 \zeta_{6} q^{4} $ $ + ( 9 - 9 \zeta_{6} ) q^{5} $ $ -10 q^{6} $ $ + ( -7 - 14 \zeta_{6} ) q^{7} $ $ + 8 q^{8} $ $ + ( 2 - 2 \zeta_{6} ) q^{9} $ $+O(q^{10})$	$ q$ $ + ( -2 + 2 \zeta_{6} ) q^{2} $ $ + 5 \zeta_{6} q^{3} $ $ -4 \zeta_{6} q^{4} $ $ + ( 9 - 9 \zeta_{6} ) q^{5} $ $ -10 q^{6} $ $ + ( -7 - 14 \zeta_{6} ) q^{7} $ $ + 8 q^{8} $ $ + ( 2 - 2 \zeta_{6} ) q^{9} $ $ + 18 \zeta_{6} q^{10} $ $ + 57 \zeta_{6} q^{11} $ $ + ( 20 - 20 \zeta_{6} ) q^{12} $ $ -70 q^{13} $ $ + ( 42 - 14 \zeta_{6} ) q^{14} $ $ + 45 q^{15} $ $ + ( -16 + 16 \zeta_{6} ) q^{16} $ $ -51 \zeta_{6} q^{17} $ $ + 4 \zeta_{6} q^{18} $ $ + ( -5 + 5 \zeta_{6} ) q^{19} $ $ -36 q^{20} $ $ + ( 70 - 105 \zeta_{6} ) q^{21} $ $ -114 q^{22} $ $ + ( -69 + 69 \zeta_{6} ) q^{23} $ $ + 40 \zeta_{6} q^{24} $ $ + 44 \zeta_{6} q^{25} $ $ + ( 140 - 140 \zeta_{6} ) q^{26} $ $ + 145 q^{27} $ $ + ( -56 + 84 \zeta_{6} ) q^{28} $ $ + 114 q^{29} $ $ + ( -90 + 90 \zeta_{6} ) q^{30} $ $ -23 \zeta_{6} q^{31} $ $ -32 \zeta_{6} q^{32} $ $ + ( -285 + 285 \zeta_{6} ) q^{33} $ $ + 102 q^{34} $ $ + ( -189 + 63 \zeta_{6} ) q^{35} $ $ -8 q^{36} $ $ + ( 253 - 253 \zeta_{6} ) q^{37} $ $ -10 \zeta_{6} q^{38} $ $ -350 \zeta_{6} q^{39} $ $ + ( 72 - 72 \zeta_{6} ) q^{40} $ $ -42 q^{41} $ $ + ( 70 + 140 \zeta_{6} ) q^{42} $ $ -124 q^{43} $ $ + ( 228 - 228 \zeta_{6} ) q^{44} $ $ -18 \zeta_{6} q^{45} $ $ -138 \zeta_{6} q^{46} $ $ + ( -201 + 201 \zeta_{6} ) q^{47} $ $ -80 q^{48} $ $ + ( -147 + 392 \zeta_{6} ) q^{49} $ $ -88 q^{50} $ $ + ( 255 - 255 \zeta_{6} ) q^{51} $ $ + 280 \zeta_{6} q^{52} $ $ + 393 \zeta_{6} q^{53} $ $ + ( -290 + 290 \zeta_{6} ) q^{54} $ $ + 513 q^{55} $ $ + ( -56 - 112 \zeta_{6} ) q^{56} $ $ -25 q^{57} $ $ + ( -228 + 228 \zeta_{6} ) q^{58} $ $ -219 \zeta_{6} q^{59} $ $ -180 \zeta_{6} q^{60} $ $ + ( 709 - 709 \zeta_{6} ) q^{61} $ $ + 46 q^{62} $ $ + ( -42 + 14 \zeta_{6} ) q^{63} $ $ + 64 q^{64} $ $ + ( -630 + 630 \zeta_{6} ) q^{65} $ $ -570 \zeta_{6} q^{66} $ $ -419 \zeta_{6} q^{67} $ $ + ( -204 + 204 \zeta_{6} ) q^{68} $ $ -345 q^{69} $ $ + ( 252 - 378 \zeta_{6} ) q^{70} $ $ -96 q^{71} $ $ + ( 16 - 16 \zeta_{6} ) q^{72} $ $ + 313 \zeta_{6} q^{73} $ $ + 506 \zeta_{6} q^{74} $ $ + ( -220 + 220 \zeta_{6} ) q^{75} $ $ + 20 q^{76} $ $ + ( 798 - 1197 \zeta_{6} ) q^{77} $ $ + 700 q^{78} $ $ + ( -461 + 461 \zeta_{6} ) q^{79} $ $ + 144 \zeta_{6} q^{80} $ $ + 671 \zeta_{6} q^{81} $ $ + ( 84 - 84 \zeta_{6} ) q^{82} $ $ -588 q^{83} $ $ + ( -420 + 140 \zeta_{6} ) q^{84} $ $ -459 q^{85} $ $ + ( 248 - 248 \zeta_{6} ) q^{86} $ $ + 570 \zeta_{6} q^{87} $ $ + 456 \zeta_{6} q^{88} $ $ + ( 1017 - 1017 \zeta_{6} ) q^{89} $ $ + 36 q^{90} $ $ + ( 490 + 980 \zeta_{6} ) q^{91} $ $ + 276 q^{92} $ $ + ( 115 - 115 \zeta_{6} ) q^{93} $ $ -402 \zeta_{6} q^{94} $ $ + 45 \zeta_{6} q^{95} $ $ + ( 160 - 160 \zeta_{6} ) q^{96} $ $ -1834 q^{97} $ $ + ( -490 - 294 \zeta_{6} ) q^{98} $ $ + 114 q^{99} $ $+O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2q $ $\mathstrut -\mathstrut 2q^{2} $ $\mathstrut +\mathstrut 5q^{3} $ $\mathstrut -\mathstrut 4q^{4} $ $\mathstrut +\mathstrut 9q^{5} $ $\mathstrut -\mathstrut 20q^{6} $ $\mathstrut -\mathstrut 28q^{7} $ $\mathstrut +\mathstrut 16q^{8} $ $\mathstrut +\mathstrut 2q^{9} $ $\mathstrut +\mathstrut O(q^{10}) $	$2q $ $\mathstrut -\mathstrut 2q^{2} $ $\mathstrut +\mathstrut 5q^{3} $ $\mathstrut -\mathstrut 4q^{4} $ $\mathstrut +\mathstrut 9q^{5} $ $\mathstrut -\mathstrut 20q^{6} $ $\mathstrut -\mathstrut 28q^{7} $ $\mathstrut +\mathstrut 16q^{8} $ $\mathstrut +\mathstrut 2q^{9} $ $\mathstrut +\mathstrut 18q^{10} $ $\mathstrut +\mathstrut 57q^{11} $ $\mathstrut +\mathstrut 20q^{12} $ $\mathstrut -\mathstrut 140q^{13} $ $\mathstrut +\mathstrut 70q^{14} $ $\mathstrut +\mathstrut 90q^{15} $ $\mathstrut -\mathstrut 16q^{16} $ $\mathstrut -\mathstrut 51q^{17} $ $\mathstrut +\mathstrut 4q^{18} $ $\mathstrut -\mathstrut 5q^{19} $ $\mathstrut -\mathstrut 72q^{20} $ $\mathstrut +\mathstrut 35q^{21} $ $\mathstrut -\mathstrut 228q^{22} $ $\mathstrut -\mathstrut 69q^{23} $ $\mathstrut +\mathstrut 40q^{24} $ $\mathstrut +\mathstrut 44q^{25} $ $\mathstrut +\mathstrut 140q^{26} $ $\mathstrut +\mathstrut 290q^{27} $ $\mathstrut -\mathstrut 28q^{28} $ $\mathstrut +\mathstrut 228q^{29} $ $\mathstrut -\mathstrut 90q^{30} $ $\mathstrut -\mathstrut 23q^{31} $ $\mathstrut -\mathstrut 32q^{32} $ $\mathstrut -\mathstrut 285q^{33} $ $\mathstrut +\mathstrut 204q^{34} $ $\mathstrut -\mathstrut 315q^{35} $ $\mathstrut -\mathstrut 16q^{36} $ $\mathstrut +\mathstrut 253q^{37} $ $\mathstrut -\mathstrut 10q^{38} $ $\mathstrut -\mathstrut 350q^{39} $ $\mathstrut +\mathstrut 72q^{40} $ $\mathstrut -\mathstrut 84q^{41} $ $\mathstrut +\mathstrut 280q^{42} $ $\mathstrut -\mathstrut 248q^{43} $ $\mathstrut +\mathstrut 228q^{44} $ $\mathstrut -\mathstrut 18q^{45} $ $\mathstrut -\mathstrut 138q^{46} $ $\mathstrut -\mathstrut 201q^{47} $ $\mathstrut -\mathstrut 160q^{48} $ $\mathstrut +\mathstrut 98q^{49} $ $\mathstrut -\mathstrut 176q^{50} $ $\mathstrut +\mathstrut 255q^{51} $ $\mathstrut +\mathstrut 280q^{52} $ $\mathstrut +\mathstrut 393q^{53} $ $\mathstrut -\mathstrut 290q^{54} $ $\mathstrut +\mathstrut 1026q^{55} $ $\mathstrut -\mathstrut 224q^{56} $ $\mathstrut -\mathstrut 50q^{57} $ $\mathstrut -\mathstrut 228q^{58} $ $\mathstrut -\mathstrut 219q^{59} $ $\mathstrut -\mathstrut 180q^{60} $ $\mathstrut +\mathstrut 709q^{61} $ $\mathstrut +\mathstrut 92q^{62} $ $\mathstrut -\mathstrut 70q^{63} $ $\mathstrut +\mathstrut 128q^{64} $ $\mathstrut -\mathstrut 630q^{65} $ $\mathstrut -\mathstrut 570q^{66} $ $\mathstrut -\mathstrut 419q^{67} $ $\mathstrut -\mathstrut 204q^{68} $ $\mathstrut -\mathstrut 690q^{69} $ $\mathstrut +\mathstrut 126q^{70} $ $\mathstrut -\mathstrut 192q^{71} $ $\mathstrut +\mathstrut 16q^{72} $ $\mathstrut +\mathstrut 313q^{73} $ $\mathstrut +\mathstrut 506q^{74} $ $\mathstrut -\mathstrut 220q^{75} $ $\mathstrut +\mathstrut 40q^{76} $ $\mathstrut +\mathstrut 399q^{77} $ $\mathstrut +\mathstrut 1400q^{78} $ $\mathstrut -\mathstrut 461q^{79} $ $\mathstrut +\mathstrut 144q^{80} $ $\mathstrut +\mathstrut 671q^{81} $ $\mathstrut +\mathstrut 84q^{82} $ $\mathstrut -\mathstrut 1176q^{83} $ $\mathstrut -\mathstrut 700q^{84} $ $\mathstrut -\mathstrut 918q^{85} $ $\mathstrut +\mathstrut 248q^{86} $ $\mathstrut +\mathstrut 570q^{87} $ $\mathstrut +\mathstrut 456q^{88} $ $\mathstrut +\mathstrut 1017q^{89} $ $\mathstrut +\mathstrut 72q^{90} $ $\mathstrut +\mathstrut 1960q^{91} $ $\mathstrut +\mathstrut 552q^{92} $ $\mathstrut +\mathstrut 115q^{93} $ $\mathstrut -\mathstrut 402q^{94} $ $\mathstrut +\mathstrut 45q^{95} $ $\mathstrut +\mathstrut 160q^{96} $ $\mathstrut -\mathstrut 3668q^{97} $ $\mathstrut -\mathstrut 1274q^{98} $ $\mathstrut +\mathstrut 228q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Character Values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1 + \zeta_{6}$

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} $

9.1

0.500000	+	0.866025i
0.500000	−	0.866025i

−1.00000

1.73205i

2.50000

4.33013i

−2.00000

−

3.46410i

4.50000

−

7.79423i

−10.0000

−14.0000

−

12.1244i

8.00000

1.00000

−

1.73205i

9.00000

15.5885i

11.1

−1.00000

−

1.73205i

2.50000

−

4.33013i

−2.00000

3.46410i

4.50000

7.79423i

−10.0000

−14.0000

12.1244i

8.00000

1.00000

1.73205i

9.00000

−

15.5885i

Inner twists

Char. orbit	Parity	Mult.	Self Twist	Proved
1.a	Even	1	trivial	yes
7.c	Even	1		yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator $T_{3}^{2} $ $\mathstrut -\mathstrut 5 T_{3} $ $\mathstrut +\mathstrut 25 $ acting on $S_{4}^{\mathrm{new}}(14, [\chi])$.

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Character orbit:	\([\chi]\)	=	14.c (of order \(3\) and degree \(2\))

\(f(q)\)	\(=\)	\( q\) \( + ( -2 + 2 \zeta_{6} ) q^{2} \) \( + 5 \zeta_{6} q^{3} \) \( -4 \zeta_{6} q^{4} \) \( + ( 9 - 9 \zeta_{6} ) q^{5} \) \( -10 q^{6} \) \( + ( -7 - 14 \zeta_{6} ) q^{7} \) \( + 8 q^{8} \) \( + ( 2 - 2 \zeta_{6} ) q^{9} \) \(+O(q^{10})\)	\( q\) \( + ( -2 + 2 \zeta_{6} ) q^{2} \) \( + 5 \zeta_{6} q^{3} \) \( -4 \zeta_{6} q^{4} \) \( + ( 9 - 9 \zeta_{6} ) q^{5} \) \( -10 q^{6} \) \( + ( -7 - 14 \zeta_{6} ) q^{7} \) \( + 8 q^{8} \) \( + ( 2 - 2 \zeta_{6} ) q^{9} \) \( + 18 \zeta_{6} q^{10} \) \( + 57 \zeta_{6} q^{11} \) \( + ( 20 - 20 \zeta_{6} ) q^{12} \) \( -70 q^{13} \) \( + ( 42 - 14 \zeta_{6} ) q^{14} \) \( + 45 q^{15} \) \( + ( -16 + 16 \zeta_{6} ) q^{16} \) \( -51 \zeta_{6} q^{17} \) \( + 4 \zeta_{6} q^{18} \) \( + ( -5 + 5 \zeta_{6} ) q^{19} \) \( -36 q^{20} \) \( + ( 70 - 105 \zeta_{6} ) q^{21} \) \( -114 q^{22} \) \( + ( -69 + 69 \zeta_{6} ) q^{23} \) \( + 40 \zeta_{6} q^{24} \) \( + 44 \zeta_{6} q^{25} \) \( + ( 140 - 140 \zeta_{6} ) q^{26} \) \( + 145 q^{27} \) \( + ( -56 + 84 \zeta_{6} ) q^{28} \) \( + 114 q^{29} \) \( + ( -90 + 90 \zeta_{6} ) q^{30} \) \( -23 \zeta_{6} q^{31} \) \( -32 \zeta_{6} q^{32} \) \( + ( -285 + 285 \zeta_{6} ) q^{33} \) \( + 102 q^{34} \) \( + ( -189 + 63 \zeta_{6} ) q^{35} \) \( -8 q^{36} \) \( + ( 253 - 253 \zeta_{6} ) q^{37} \) \( -10 \zeta_{6} q^{38} \) \( -350 \zeta_{6} q^{39} \) \( + ( 72 - 72 \zeta_{6} ) q^{40} \) \( -42 q^{41} \) \( + ( 70 + 140 \zeta_{6} ) q^{42} \) \( -124 q^{43} \) \( + ( 228 - 228 \zeta_{6} ) q^{44} \) \( -18 \zeta_{6} q^{45} \) \( -138 \zeta_{6} q^{46} \) \( + ( -201 + 201 \zeta_{6} ) q^{47} \) \( -80 q^{48} \) \( + ( -147 + 392 \zeta_{6} ) q^{49} \) \( -88 q^{50} \) \( + ( 255 - 255 \zeta_{6} ) q^{51} \) \( + 280 \zeta_{6} q^{52} \) \( + 393 \zeta_{6} q^{53} \) \( + ( -290 + 290 \zeta_{6} ) q^{54} \) \( + 513 q^{55} \) \( + ( -56 - 112 \zeta_{6} ) q^{56} \) \( -25 q^{57} \) \( + ( -228 + 228 \zeta_{6} ) q^{58} \) \( -219 \zeta_{6} q^{59} \) \( -180 \zeta_{6} q^{60} \) \( + ( 709 - 709 \zeta_{6} ) q^{61} \) \( + 46 q^{62} \) \( + ( -42 + 14 \zeta_{6} ) q^{63} \) \( + 64 q^{64} \) \( + ( -630 + 630 \zeta_{6} ) q^{65} \) \( -570 \zeta_{6} q^{66} \) \( -419 \zeta_{6} q^{67} \) \( + ( -204 + 204 \zeta_{6} ) q^{68} \) \( -345 q^{69} \) \( + ( 252 - 378 \zeta_{6} ) q^{70} \) \( -96 q^{71} \) \( + ( 16 - 16 \zeta_{6} ) q^{72} \) \( + 313 \zeta_{6} q^{73} \) \( + 506 \zeta_{6} q^{74} \) \( + ( -220 + 220 \zeta_{6} ) q^{75} \) \( + 20 q^{76} \) \( + ( 798 - 1197 \zeta_{6} ) q^{77} \) \( + 700 q^{78} \) \( + ( -461 + 461 \zeta_{6} ) q^{79} \) \( + 144 \zeta_{6} q^{80} \) \( + 671 \zeta_{6} q^{81} \) \( + ( 84 - 84 \zeta_{6} ) q^{82} \) \( -588 q^{83} \) \( + ( -420 + 140 \zeta_{6} ) q^{84} \) \( -459 q^{85} \) \( + ( 248 - 248 \zeta_{6} ) q^{86} \) \( + 570 \zeta_{6} q^{87} \) \( + 456 \zeta_{6} q^{88} \) \( + ( 1017 - 1017 \zeta_{6} ) q^{89} \) \( + 36 q^{90} \) \( + ( 490 + 980 \zeta_{6} ) q^{91} \) \( + 276 q^{92} \) \( + ( 115 - 115 \zeta_{6} ) q^{93} \) \( -402 \zeta_{6} q^{94} \) \( + 45 \zeta_{6} q^{95} \) \( + ( 160 - 160 \zeta_{6} ) q^{96} \) \( -1834 q^{97} \) \( + ( -490 - 294 \zeta_{6} ) q^{98} \) \( + 114 q^{99} \) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)	\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 57q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut -\mathstrut 140q^{13} \) \(\mathstrut +\mathstrut 70q^{14} \) \(\mathstrut +\mathstrut 90q^{15} \) \(\mathstrut -\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 51q^{17} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 72q^{20} \) \(\mathstrut +\mathstrut 35q^{21} \) \(\mathstrut -\mathstrut 228q^{22} \) \(\mathstrut -\mathstrut 69q^{23} \) \(\mathstrut +\mathstrut 40q^{24} \) \(\mathstrut +\mathstrut 44q^{25} \) \(\mathstrut +\mathstrut 140q^{26} \) \(\mathstrut +\mathstrut 290q^{27} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut +\mathstrut 228q^{29} \) \(\mathstrut -\mathstrut 90q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 285q^{33} \) \(\mathstrut +\mathstrut 204q^{34} \) \(\mathstrut -\mathstrut 315q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut +\mathstrut 253q^{37} \) \(\mathstrut -\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 350q^{39} \) \(\mathstrut +\mathstrut 72q^{40} \) \(\mathstrut -\mathstrut 84q^{41} \) \(\mathstrut +\mathstrut 280q^{42} \) \(\mathstrut -\mathstrut 248q^{43} \) \(\mathstrut +\mathstrut 228q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 138q^{46} \) \(\mathstrut -\mathstrut 201q^{47} \) \(\mathstrut -\mathstrut 160q^{48} \) \(\mathstrut +\mathstrut 98q^{49} \) \(\mathstrut -\mathstrut 176q^{50} \) \(\mathstrut +\mathstrut 255q^{51} \) \(\mathstrut +\mathstrut 280q^{52} \) \(\mathstrut +\mathstrut 393q^{53} \) \(\mathstrut -\mathstrut 290q^{54} \) \(\mathstrut +\mathstrut 1026q^{55} \) \(\mathstrut -\mathstrut 224q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut -\mathstrut 228q^{58} \) \(\mathstrut -\mathstrut 219q^{59} \) \(\mathstrut -\mathstrut 180q^{60} \) \(\mathstrut +\mathstrut 709q^{61} \) \(\mathstrut +\mathstrut 92q^{62} \) \(\mathstrut -\mathstrut 70q^{63} \) \(\mathstrut +\mathstrut 128q^{64} \) \(\mathstrut -\mathstrut 630q^{65} \) \(\mathstrut -\mathstrut 570q^{66} \) \(\mathstrut -\mathstrut 419q^{67} \) \(\mathstrut -\mathstrut 204q^{68} \) \(\mathstrut -\mathstrut 690q^{69} \) \(\mathstrut +\mathstrut 126q^{70} \) \(\mathstrut -\mathstrut 192q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut +\mathstrut 313q^{73} \) \(\mathstrut +\mathstrut 506q^{74} \) \(\mathstrut -\mathstrut 220q^{75} \) \(\mathstrut +\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 399q^{77} \) \(\mathstrut +\mathstrut 1400q^{78} \) \(\mathstrut -\mathstrut 461q^{79} \) \(\mathstrut +\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 671q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut -\mathstrut 1176q^{83} \) \(\mathstrut -\mathstrut 700q^{84} \) \(\mathstrut -\mathstrut 918q^{85} \) \(\mathstrut +\mathstrut 248q^{86} \) \(\mathstrut +\mathstrut 570q^{87} \) \(\mathstrut +\mathstrut 456q^{88} \) \(\mathstrut +\mathstrut 1017q^{89} \) \(\mathstrut +\mathstrut 72q^{90} \) \(\mathstrut +\mathstrut 1960q^{91} \) \(\mathstrut +\mathstrut 552q^{92} \) \(\mathstrut +\mathstrut 115q^{93} \) \(\mathstrut -\mathstrut 402q^{94} \) \(\mathstrut +\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 160q^{96} \) \(\mathstrut -\mathstrut 3668q^{97} \) \(\mathstrut -\mathstrut 1274q^{98} \) \(\mathstrut +\mathstrut 228q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

\(n\)	\(3\)
\(\chi(n)\)	\(-1 + \zeta_{6}\)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
Format:

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Newspace parameters

Newform invariants

$q$-expansion

Character Values

Embeddings

Inner twists

Hecke kernels

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	14.4.c.a

Level	14
Weight	4
Character orbit	14.c
Analytic conductor	0.826
Analytic rank	0
Dimension	2
CM	No
Inner twists	2

Self dual:	No
Analytic conductor:	\(0.82602674008\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$