Embedded newform 891.1.c.b.406.1

• Label: 891.1.c.b.406.1
• Level: $891$
• Weight: $1$
• Character: 891.406
• Self dual: yes
• Analytic conductor: $0.445$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	891.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.444666926256\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 99)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.891.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.2381643.1
Stark unit:	Root of $x^{6} - 510x^{5} - 20298x^{4} - 301718x^{3} - 20298x^{2} - 510x + 1$

Embedding invariants

Embedding label			406.1
Character	\(\chi\)	\(=\)	891.406

$q$-expansion

\(f(q)\)

\(=\)

\(q+1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{11} +1.00000 q^{16} +1.00000 q^{20} -2.00000 q^{23} -1.00000 q^{31} -1.00000 q^{37} -1.00000 q^{44} +1.00000 q^{47} +1.00000 q^{49} +1.00000 q^{53} -1.00000 q^{55} +1.00000 q^{59} +1.00000 q^{64} -1.00000 q^{67} +1.00000 q^{71} +1.00000 q^{80} -2.00000 q^{89} -2.00000 q^{92} -1.00000 q^{97} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\)	\(244\)	\(650\)
\(\chi(n)\)	\(-1\)	\(1\)

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)

\(p\)	\(a_p\)	\(a_p / p^{(k-1)/2}\)	\( \alpha_p\)			\( \theta_p \)
\(2\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(3\)	0	0
			\(5\)	1.00000	1.00000	0.500000	−	0.866025i	\(-0.333333\pi\)
0.500000	+	0.866025i				\(0.333333\pi\)
\(7\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(11\)	−1.00000	−1.00000
			\(13\)	0	0	1.00000			\(0\)
−1.00000						\(\pi\)
\(17\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(19\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(23\)	−2.00000	−2.00000	−1.00000			\(\pi\)
			−1.00000			\(\pi\)
\(29\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(31\)	−1.00000	−1.00000	−0.500000	−	0.866025i	\(-0.666667\pi\)
			−0.500000	+	0.866025i	\(0.666667\pi\)
\(37\)	−1.00000	−1.00000	−0.500000	−	0.866025i	\(-0.666667\pi\)
			−0.500000	+	0.866025i	\(0.666667\pi\)
\(41\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(43\)	0	0	1.00000			\(0\)
			−1.00000			\(\pi\)
\(47\)	1.00000	1.00000	0.500000	−	0.866025i	\(-0.333333\pi\)
			0.500000	+	0.866025i	\(0.333333\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.1.c.b.406.1		1
3.2	odd	2		891.1.c.a.406.1		1
9.2	odd	6		99.1.h.a.76.1	yes	2
9.4	even	3		297.1.h.a.208.1		2
9.5	odd	6		99.1.h.a.43.1	✓	2
9.7	even	3		297.1.h.a.10.1		2
11.10	odd	2	CM	891.1.c.b.406.1		1
33.32	even	2		891.1.c.a.406.1		1
36.11	even	6		1584.1.bf.b.769.1		2
36.23	even	6		1584.1.bf.b.241.1		2
45.2	even	12		2475.1.t.a.274.2		4
45.14	odd	6		2475.1.y.a.1726.1		2
45.23	even	12		2475.1.t.a.1924.2		4
45.29	odd	6		2475.1.y.a.76.1		2
45.32	even	12		2475.1.t.a.1924.1		4
45.38	even	12		2475.1.t.a.274.1		4
99.2	even	30		1089.1.s.a.40.1		8
99.4	even	15		3267.1.w.a.1909.1		8
99.5	odd	30		1089.1.s.a.844.1		8
99.7	odd	30		3267.1.w.a.820.1		8
99.13	odd	30		3267.1.w.a.1855.1		8
99.14	odd	30		1089.1.s.a.475.1		8
99.16	even	15		3267.1.w.a.118.1		8
99.20	odd	30		1089.1.s.a.40.1		8
99.25	even	15		3267.1.w.a.1927.1		8
99.29	even	30		1089.1.s.a.94.1		8
99.31	even	15		3267.1.w.a.1855.1		8
99.32	even	6		99.1.h.a.43.1	✓	2
99.38	odd	30		1089.1.s.a.481.1		8
99.40	odd	30		3267.1.w.a.1909.1		8
99.41	even	30		1089.1.s.a.475.1		8
99.43	odd	6		297.1.h.a.10.1		2
99.47	odd	30		1089.1.s.a.112.1		8
99.49	even	15		3267.1.w.a.1207.1		8
99.50	even	30		1089.1.s.a.844.1		8
99.52	odd	30		3267.1.w.a.1927.1		8
99.58	even	15		3267.1.w.a.3016.1		8
99.59	odd	30		1089.1.s.a.457.1		8
99.61	odd	30		3267.1.w.a.118.1		8
99.65	even	6		99.1.h.a.76.1	yes	2
99.68	even	30		1089.1.s.a.403.1		8
99.70	even	15		3267.1.w.a.820.1		8
99.74	even	30		1089.1.s.a.112.1		8
99.76	odd	6		297.1.h.a.208.1		2
99.79	odd	30		3267.1.w.a.766.1		8
99.83	even	30		1089.1.s.a.481.1		8
99.85	odd	30		3267.1.w.a.3016.1		8
99.86	odd	30		1089.1.s.a.403.1		8
99.92	odd	30		1089.1.s.a.94.1		8
99.94	odd	30		3267.1.w.a.1207.1		8
99.95	even	30		1089.1.s.a.457.1		8
99.97	even	15		3267.1.w.a.766.1		8
396.131	odd	6		1584.1.bf.b.241.1		2
396.263	odd	6		1584.1.bf.b.769.1		2
495.32	odd	12		2475.1.t.a.1924.1		4
495.164	even	6		2475.1.y.a.76.1		2
495.263	odd	12		2475.1.t.a.274.1		4
495.329	even	6		2475.1.y.a.1726.1		2
495.362	odd	12		2475.1.t.a.274.2		4
495.428	odd	12		2475.1.t.a.1924.2		4

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.1.h.a.43.1	✓	2	9.5	odd	6
99.1.h.a.43.1	✓	2	99.32	even	6
99.1.h.a.76.1	yes	2	9.2	odd	6
99.1.h.a.76.1	yes	2	99.65	even	6
297.1.h.a.10.1		2	9.7	even	3
297.1.h.a.10.1		2	99.43	odd	6
297.1.h.a.208.1		2	9.4	even	3
297.1.h.a.208.1		2	99.76	odd	6
891.1.c.a.406.1		1	3.2	odd	2
891.1.c.a.406.1		1	33.32	even	2
891.1.c.b.406.1		1	1.1	even	1	trivial
891.1.c.b.406.1		1	11.10	odd	2	CM
1089.1.s.a.40.1		8	99.2	even	30
1089.1.s.a.40.1		8	99.20	odd	30
1089.1.s.a.94.1		8	99.29	even	30
1089.1.s.a.94.1		8	99.92	odd	30
1089.1.s.a.112.1		8	99.47	odd	30
1089.1.s.a.112.1		8	99.74	even	30
1089.1.s.a.403.1		8	99.68	even	30
1089.1.s.a.403.1		8	99.86	odd	30
1089.1.s.a.457.1		8	99.59	odd	30
1089.1.s.a.457.1		8	99.95	even	30
1089.1.s.a.475.1		8	99.14	odd	30
1089.1.s.a.475.1		8	99.41	even	30
1089.1.s.a.481.1		8	99.38	odd	30
1089.1.s.a.481.1		8	99.83	even	30
1089.1.s.a.844.1		8	99.5	odd	30
1089.1.s.a.844.1		8	99.50	even	30
1584.1.bf.b.241.1		2	36.23	even	6
1584.1.bf.b.241.1		2	396.131	odd	6
1584.1.bf.b.769.1		2	36.11	even	6
1584.1.bf.b.769.1		2	396.263	odd	6
2475.1.t.a.274.1		4	45.38	even	12
2475.1.t.a.274.1		4	495.263	odd	12
2475.1.t.a.274.2		4	45.2	even	12
2475.1.t.a.274.2		4	495.362	odd	12
2475.1.t.a.1924.1		4	45.32	even	12
2475.1.t.a.1924.1		4	495.32	odd	12
2475.1.t.a.1924.2		4	45.23	even	12
2475.1.t.a.1924.2		4	495.428	odd	12
2475.1.y.a.76.1		2	45.29	odd	6
2475.1.y.a.76.1		2	495.164	even	6
2475.1.y.a.1726.1		2	45.14	odd	6
2475.1.y.a.1726.1		2	495.329	even	6
3267.1.w.a.118.1		8	99.16	even	15
3267.1.w.a.118.1		8	99.61	odd	30
3267.1.w.a.766.1		8	99.79	odd	30
3267.1.w.a.766.1		8	99.97	even	15
3267.1.w.a.820.1		8	99.7	odd	30
3267.1.w.a.820.1		8	99.70	even	15
3267.1.w.a.1207.1		8	99.49	even	15
3267.1.w.a.1207.1		8	99.94	odd	30
3267.1.w.a.1855.1		8	99.13	odd	30
3267.1.w.a.1855.1		8	99.31	even	15
3267.1.w.a.1909.1		8	99.4	even	15
3267.1.w.a.1909.1		8	99.40	odd	30
3267.1.w.a.1927.1		8	99.25	even	15
3267.1.w.a.1927.1		8	99.52	odd	30
3267.1.w.a.3016.1		8	99.58	even	15
3267.1.w.a.3016.1		8	99.85	odd	30