Embedded newform 91.10.f.b.22.5

• Label: 91.10.f.b.22.5
• Level: $91$
• Weight: $10$
• Character: 91.22
• Analytic conductor: $46.868$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(46.8682610909\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.5
Character	\(\chi\)	\(=\)	91.22
Dual form			91.10.f.b.29.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-16.9313 + 29.3259i) q^{2} +(-117.012 + 202.670i) q^{3} +(-317.339 - 549.648i) q^{4} -1830.35 q^{5} +(-3962.33 - 6862.95i) q^{6} +(1200.50 + 2079.33i) q^{7} +4154.21 q^{8} +(-17542.0 - 30383.6i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{2} - 4 q^{3} - 8448 q^{4} - 4016 q^{5} + 1497 q^{6} + 76832 q^{7} - 33654 q^{8} - 196012 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\)	\(15\)	\(66\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−16.9313	+	29.3259i	−0.748266	+	1.29603i	0.200388	+	0.979717i	\(0.435780\pi\)
							−0.948653	+	0.316318i	\(0.897554\pi\)
\(3\)	−117.012	+	202.670i	−0.834034	+	1.44459i	0.0607809	+	0.998151i	\(0.480641\pi\)
							−0.894815	+	0.446438i	\(0.852692\pi\)
\(5\)	−1830.35			−1.30969			−0.654847	−	0.755761i	\(-0.727267\pi\)
							−0.654847	+	0.755761i	\(0.727267\pi\)
\(7\)	1200.50	+	2079.33i	0.188982	+	0.327327i
							\(11\)	−5163.52	+	8943.47i	−0.106336	+	0.184179i	−0.914283	−	0.405076i	\(-0.867245\pi\)
0.807948	+	0.589254i	\(0.200578\pi\)
\(13\)	−92696.3	−	44854.1i	−0.900155	−	0.435570i
							\(17\)	−34417.2	−	59612.3i	−0.0999436	−	0.173107i	0.811717	−	0.584050i	\(-0.198533\pi\)
−0.911661	+	0.410943i	\(0.865200\pi\)
\(19\)	119047.	+	206196.i	0.209569	+	0.362985i	0.951579	−	0.307405i	\(-0.0994605\pi\)
							−0.742010	+	0.670389i	\(0.766127\pi\)
\(23\)	−708630.	+	1.22738e6i	−0.528012	+	0.914544i	0.471454	+	0.881890i	\(0.343729\pi\)
							−0.999467	+	0.0326537i	\(0.989604\pi\)
\(29\)	−1.85455e6	+	3.21218e6i	−0.486910	+	0.843352i	−0.999887	−	0.0150500i	\(-0.995209\pi\)
							0.512977	+	0.858402i	\(0.328543\pi\)
\(31\)	3.41952e6			0.665024			0.332512	−	0.943099i	\(-0.392104\pi\)
							0.332512	+	0.943099i	\(0.392104\pi\)
\(37\)	3.72041e6	−	6.44394e6i	0.326350	−	0.565254i	−0.655435	−	0.755252i	\(-0.727515\pi\)
							0.981785	+	0.189997i	\(0.0608479\pi\)
\(41\)	9.19877e6	−	1.59327e7i	0.508396	−	0.880568i	−0.491556	−	0.870846i	\(-0.663572\pi\)
							0.999953	−	0.00972255i	\(-0.00309483\pi\)
\(43\)	−1.74677e7	−	3.02549e7i	−0.779161	−	1.34955i	−0.932426	−	0.361361i	\(-0.882312\pi\)
							0.153265	−	0.988185i	\(-0.451021\pi\)
\(47\)	−6.01716e7			−1.79867			−0.899334	−	0.437263i	\(-0.855948\pi\)
							−0.899334	+	0.437263i	\(0.855948\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.f.b.22.5	✓	64
13.3	even	3	inner	91.10.f.b.29.5	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.f.b.22.5	✓	64	1.1	even	1	trivial
91.10.f.b.29.5	yes	64	13.3	even	3	inner