Newform orbit 891.2.n.h

• Label: 891.2.n.h
• Level: $891$
• Weight: $2$
• Character orbit: 891.n
• Analytic conductor: $7.115$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $8$

Newspace parameters

Level:	$N$	$=$	$891 = 3^{4} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
136.1	−2.09957	+	0.934789i		0		2.19611	−	2.43902i	−1.55025	−	0.690215i		0		−0.203124	−	0.0431753i	−0.910502	+	2.80224i		0		3.90006
136.2	−0.288796	+	0.128580i		0		−1.27139	+	1.41202i	3.70483	+	1.64949i		0		−3.33585	−	0.709056i	0.380991	−	1.17257i		0		−1.28203
136.3	0.288796	−	0.128580i		0		−1.27139	+	1.41202i	−3.70483	−	1.64949i		0		−3.33585	−	0.709056i	−0.380991	+	1.17257i		0		−1.28203
136.4	2.09957	−	0.934789i		0		2.19611	−	2.43902i	1.55025	+	0.690215i		0		−0.203124	−	0.0431753i	0.910502	−	2.80224i		0		3.90006
190.1	−2.09957	−	0.934789i		0		2.19611	+	2.43902i	−1.55025	+	0.690215i		0		−0.203124	+	0.0431753i	−0.910502	−	2.80224i		0		3.90006
190.2	−0.288796	−	0.128580i		0		−1.27139	−	1.41202i	3.70483	−	1.64949i		0		−3.33585	+	0.709056i	0.380991	+	1.17257i		0		−1.28203
190.3	0.288796	+	0.128580i		0		−1.27139	−	1.41202i	−3.70483	+	1.64949i		0		−3.33585	+	0.709056i	−0.380991	−	1.17257i		0		−1.28203
190.4	2.09957	+	0.934789i		0		2.19611	+	2.43902i	1.55025	−	0.690215i		0		−0.203124	+	0.0431753i	0.910502	+	2.80224i		0		3.90006
379.1	−2.40657	−	0.511531i		0		3.70281	+	1.64860i	−0.968153	+	0.205787i		0		−0.451792	−	4.29851i	−4.08684	−	2.96926i		0		2.43519
379.2	−1.22359	−	0.260081i		0		−0.397568	−	0.177009i	1.60550	−	0.341260i		0		0.307337	+	2.92412i	2.46446	+	1.79053i		0		−2.05323
379.3	1.22359	+	0.260081i		0		−0.397568	−	0.177009i	−1.60550	+	0.341260i		0		0.307337	+	2.92412i	−2.46446	−	1.79053i		0		−2.05323
379.4	2.40657	+	0.511531i		0		3.70281	+	1.64860i	0.968153	−	0.205787i		0		−0.451792	−	4.29851i	4.08684	+	2.96926i		0		2.43519
433.1	−0.240234	+	2.28568i		0		−3.21031	−	0.682372i	−0.177381	−	1.68766i		0		0.138953	−	0.154323i	0.910502	−	2.80224i		0		3.90006
433.2	−0.0330442	+	0.314395i		0		1.85854	+	0.395046i	0.423909	+	4.03322i		0		2.28198	−	2.53440i	−0.380991	+	1.17257i		0		−1.28203
433.3	0.0330442	−	0.314395i		0		1.85854	+	0.395046i	−0.423909	−	4.03322i		0		2.28198	−	2.53440i	0.380991	−	1.17257i		0		−1.28203
433.4	0.240234	−	2.28568i		0		−3.21031	−	0.682372i	0.177381	+	1.68766i		0		0.138953	−	0.154323i	−0.910502	+	2.80224i		0		3.90006
460.1	−1.64628	−	1.82838i		0		−0.423677	+	4.03102i	−0.662294	+	0.735552i		0		3.94852	−	1.75799i	4.08684	−	2.96926i		0		2.43519
460.2	−0.837031	−	0.929617i		0		0.0454900	−	0.432808i	1.09829	−	1.21977i		0		−2.68603	+	1.19590i	−2.46446	+	1.79053i		0		−2.05323
460.3	0.837031	+	0.929617i		0		0.0454900	−	0.432808i	−1.09829	+	1.21977i		0		−2.68603	+	1.19590i	2.46446	−	1.79053i		0		−2.05323
460.4	1.64628	+	1.82838i		0		−0.423677	+	4.03102i	0.662294	−	0.735552i		0		3.94852	−	1.75799i	−4.08684	+	2.96926i		0		2.43519

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
9.c	even	3	1	inner
9.d	odd	6	1	inner
11.c	even	5	1	inner
33.h	odd	10	1	inner
99.m	even	15	1	inner
99.n	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	891.2.n.h		32
3.b	odd	2	1	inner	891.2.n.h		32
9.c	even	3	1		297.2.f.b	✓	16
9.c	even	3	1	inner	891.2.n.h		32
9.d	odd	6	1		297.2.f.b	✓	16
9.d	odd	6	1	inner	891.2.n.h		32
11.c	even	5	1	inner	891.2.n.h		32
33.h	odd	10	1	inner	891.2.n.h		32
99.m	even	15	1		297.2.f.b	✓	16
99.m	even	15	1	inner	891.2.n.h		32
99.m	even	15	1		3267.2.a.bj		8
99.n	odd	30	1		297.2.f.b	✓	16
99.n	odd	30	1	inner	891.2.n.h		32
99.n	odd	30	1		3267.2.a.bj		8
99.o	odd	30	1		3267.2.a.bi		8
99.p	even	30	1		3267.2.a.bi		8

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
297.2.f.b	✓	16	9.c	even	3	1
297.2.f.b	✓	16	9.d	odd	6	1
297.2.f.b	✓	16	99.m	even	15	1
297.2.f.b	✓	16	99.n	odd	30	1
891.2.n.h		32	1.a	even	1	1	trivial
891.2.n.h		32	3.b	odd	2	1	inner
891.2.n.h		32	9.c	even	3	1	inner
891.2.n.h		32	9.d	odd	6	1	inner
891.2.n.h		32	11.c	even	5	1	inner
891.2.n.h		32	33.h	odd	10	1	inner
891.2.n.h		32	99.m	even	15	1	inner
891.2.n.h		32	99.n	odd	30	1	inner
3267.2.a.bi		8	99.o	odd	30	1
3267.2.a.bi		8	99.p	even	30	1
3267.2.a.bj		8	99.m	even	15	1
3267.2.a.bj		8	99.n	odd	30	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 9*T2^30 + 30*T2^28 + 39*T2^26 - 1116*T2^24 + 10994*T2^22 - 34480*T2^20 - 95164*T2^18 + 1341341*T2^16 - 3074520*T2^14 + 4852840*T2^12 - 7088350*T2^10 + 5774700*T2^8 + 435625*T2^6 - 42750*T2^4 + 3125*T2^2 + 625