Newform orbit 891.2.n.g

• Label: 891.2.n.g
• 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 - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

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	−2.13857	+	0.952153i		0		2.32863	−	2.58621i	3.27795	+	1.45944i		0		−1.12566	−	0.239267i	−1.07069	+	3.29523i		0		−8.39974
136.2	−0.974523	+	0.433886i		0		−0.576823	+	0.640627i	−1.12149	−	0.499319i		0		1.49928	+	0.318682i	0.943455	−	2.90366i		0		1.30957
136.3	0.974523	−	0.433886i		0		−0.576823	+	0.640627i	1.12149	+	0.499319i		0		1.49928	+	0.318682i	−0.943455	+	2.90366i		0		1.30957
136.4	2.13857	−	0.952153i		0		2.32863	−	2.58621i	−3.27795	−	1.45944i		0		−1.12566	−	0.239267i	1.07069	−	3.29523i		0		−8.39974
190.1	−2.13857	−	0.952153i		0		2.32863	+	2.58621i	3.27795	−	1.45944i		0		−1.12566	+	0.239267i	−1.07069	−	3.29523i		0		−8.39974
190.2	−0.974523	−	0.433886i		0		−0.576823	−	0.640627i	−1.12149	+	0.499319i		0		1.49928	−	0.318682i	0.943455	+	2.90366i		0		1.30957
190.3	0.974523	+	0.433886i		0		−0.576823	−	0.640627i	1.12149	−	0.499319i		0		1.49928	−	0.318682i	−0.943455	−	2.90366i		0		1.30957
190.4	2.13857	+	0.952153i		0		2.32863	+	2.58621i	−3.27795	+	1.45944i		0		−1.12566	+	0.239267i	1.07069	+	3.29523i		0		−8.39974
379.1	−1.93997	−	0.412354i		0		1.76637	+	0.786438i	−2.93030	+	0.622855i		0		0.431548	+	4.10590i	0.106651	+	0.0774867i		0		5.94154
379.2	−0.655019	−	0.139229i		0		−1.41743	−	0.631078i	2.70426	−	0.574808i		0		−0.157889	−	1.50221i	1.92410	+	1.39794i		0		−1.85137
379.3	0.655019	+	0.139229i		0		−1.41743	−	0.631078i	−2.70426	+	0.574808i		0		−0.157889	−	1.50221i	−1.92410	−	1.39794i		0		−1.85137
379.4	1.93997	+	0.412354i		0		1.76637	+	0.786438i	2.93030	−	0.622855i		0		0.431548	+	4.10590i	−0.106651	−	0.0774867i		0		5.94154
433.1	−0.244697	+	2.32813i		0		−3.40403	−	0.723550i	0.375065	+	3.56851i		0		0.770042	−	0.855218i	1.07069	−	3.29523i		0		−8.39974
433.2	−0.111506	+	1.06090i		0		0.843211	+	0.179230i	−0.128322	−	1.22090i		0		−1.02563	+	1.13907i	−0.943455	+	2.90366i		0		1.30957
433.3	0.111506	−	1.06090i		0		0.843211	+	0.179230i	0.128322	+	1.22090i		0		−1.02563	+	1.13907i	0.943455	−	2.90366i		0		1.30957
433.4	0.244697	−	2.32813i		0		−3.40403	−	0.723550i	−0.375065	−	3.56851i		0		0.770042	−	0.855218i	−1.07069	+	3.29523i		0		−8.39974
460.1	−1.32710	−	1.47389i		0		−0.202109	+	1.92294i	−2.00456	+	2.22629i		0		−3.77159	+	1.67922i	−0.106651	+	0.0774867i		0		5.94154
460.2	−0.448085	−	0.497649i		0		0.162183	−	1.54307i	1.84993	−	2.05455i		0		1.37990	−	0.614370i	−1.92410	+	1.39794i		0		−1.85137
460.3	0.448085	+	0.497649i		0		0.162183	−	1.54307i	−1.84993	+	2.05455i		0		1.37990	−	0.614370i	1.92410	−	1.39794i		0		−1.85137
460.4	1.32710	+	1.47389i		0		−0.202109	+	1.92294i	2.00456	−	2.22629i		0		−3.77159	+	1.67922i	0.106651	−	0.0774867i		0		5.94154

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.g		32
3.b	odd	2	1	inner	891.2.n.g		32
9.c	even	3	1		297.2.f.c	✓	16
9.c	even	3	1	inner	891.2.n.g		32
9.d	odd	6	1		297.2.f.c	✓	16
9.d	odd	6	1	inner	891.2.n.g		32
11.c	even	5	1	inner	891.2.n.g		32
33.h	odd	10	1	inner	891.2.n.g		32
99.m	even	15	1		297.2.f.c	✓	16
99.m	even	15	1	inner	891.2.n.g		32
99.m	even	15	1		3267.2.a.bg		8
99.n	odd	30	1		297.2.f.c	✓	16
99.n	odd	30	1	inner	891.2.n.g		32
99.n	odd	30	1		3267.2.a.bg		8
99.o	odd	30	1		3267.2.a.bh		8
99.p	even	30	1		3267.2.a.bh		8

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 3*T2^30 - 16*T2^28 + 211*T2^26 - 298*T2^24 - 778*T2^22 + 8748*T2^20 - 64424*T2^18 + 208101*T2^16 + 71414*T2^14 - 308312*T2^12 + 288788*T2^10 + 202882*T2^8 - 193611*T2^6 + 96074*T2^4 - 49247*T2^2 + 14641