Newform orbit 891.2.u.c

• Label: 891.2.u.c
• Level: $891$
• Weight: $2$
• Character orbit: 891.u
• Analytic conductor: $7.115$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.11467082010\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(4\) over \(\Q(\zeta_{30})\)
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 4 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
107.1	−0.254665	−	2.42297i		0		−3.84965	+	0.818267i	−3.77497	−	0.396765i		0		0.273322	−	0.246100i	1.45728	+	4.48505i		0				9.24768i
107.2	−0.0265163	−	0.252286i		0		1.89335	−	0.402444i	2.90572	+	0.305404i		0		−2.02056	+	1.81932i	−0.308515	−	0.949513i		0			−	0.741170i
107.3	0.0265163	+	0.252286i		0		1.89335	−	0.402444i	−2.90572	−	0.305404i		0		−2.02056	+	1.81932i	0.308515	+	0.949513i		0			−	0.741170i
107.4	0.254665	+	2.42297i		0		−3.84965	+	0.818267i	3.77497	+	0.396765i		0		0.273322	−	0.246100i	−1.45728	−	4.48505i		0				9.24768i
134.1	−2.29943	+	0.488759i		0		3.22139	−	1.43426i	−0.467414	+	2.19901i		0		4.02888	+	0.423453i	−2.90269	+	2.10893i		0			−	5.28492i
134.2	−0.673250	+	0.143104i		0		−1.39430	+	0.620784i	0.00833908	−	0.0392323i		0		−0.245496	−	0.0258027i	1.96356	−	1.42661i		0				0.0276065i
134.3	0.673250	−	0.143104i		0		−1.39430	+	0.620784i	−0.00833908	+	0.0392323i		0		−0.245496	−	0.0258027i	−1.96356	+	1.42661i		0				0.0276065i
134.4	2.29943	−	0.488759i		0		3.22139	−	1.43426i	0.467414	−	2.19901i		0		4.02888	+	0.423453i	2.90269	−	2.10893i		0			−	5.28492i
215.1	−1.57299	+	1.74698i		0		−0.368594	−	3.50694i	1.67069	−	1.50430i		0		−1.64772	+	3.70084i	2.90269	+	2.10893i		0				5.28492i
215.2	−0.460557	+	0.511500i		0		0.159537	+	1.51789i	−0.0298066	+	0.0268380i		0		0.100402	−	0.225507i	−1.96356	−	1.42661i		0			−	0.0276065i
215.3	0.460557	−	0.511500i		0		0.159537	+	1.51789i	0.0298066	−	0.0268380i		0		0.100402	−	0.225507i	1.96356	+	1.42661i		0			−	0.0276065i
215.4	1.57299	−	1.74698i		0		−0.368594	−	3.50694i	−1.67069	+	1.50430i		0		−1.64772	+	3.70084i	−2.90269	−	2.10893i		0				5.28492i
431.1	−1.57299	−	1.74698i		0		−0.368594	+	3.50694i	1.67069	+	1.50430i		0		−1.64772	−	3.70084i	2.90269	−	2.10893i		0			−	5.28492i
431.2	−0.460557	−	0.511500i		0		0.159537	−	1.51789i	−0.0298066	−	0.0268380i		0		0.100402	+	0.225507i	−1.96356	+	1.42661i		0				0.0276065i
431.3	0.460557	+	0.511500i		0		0.159537	−	1.51789i	0.0298066	+	0.0268380i		0		0.100402	+	0.225507i	1.96356	−	1.42661i		0				0.0276065i
431.4	1.57299	+	1.74698i		0		−0.368594	+	3.50694i	−1.67069	−	1.50430i		0		−1.64772	−	3.70084i	−2.90269	+	2.10893i		0			−	5.28492i
458.1	−0.254665	+	2.42297i		0		−3.84965	−	0.818267i	−3.77497	+	0.396765i		0		0.273322	+	0.246100i	1.45728	−	4.48505i		0			−	9.24768i
458.2	−0.0265163	+	0.252286i		0		1.89335	+	0.402444i	2.90572	−	0.305404i		0		−2.02056	−	1.81932i	−0.308515	+	0.949513i		0				0.741170i
458.3	0.0265163	−	0.252286i		0		1.89335	+	0.402444i	−2.90572	+	0.305404i		0		−2.02056	−	1.81932i	0.308515	−	0.949513i		0				0.741170i
458.4	0.254665	−	2.42297i		0		−3.84965	−	0.818267i	3.77497	−	0.396765i		0		0.273322	+	0.246100i	−1.45728	+	4.48505i		0			−	9.24768i

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.d	odd	10	1	inner
33.f	even	10	1	inner
99.o	odd	30	1	inner
99.p	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	891.2.u.c		32
3.b	odd	2	1	inner	891.2.u.c		32
9.c	even	3	1		99.2.j.a	✓	16
9.c	even	3	1	inner	891.2.u.c		32
9.d	odd	6	1		99.2.j.a	✓	16
9.d	odd	6	1	inner	891.2.u.c		32
11.d	odd	10	1	inner	891.2.u.c		32
33.f	even	10	1	inner	891.2.u.c		32
36.f	odd	6	1		1584.2.cd.c		16
36.h	even	6	1		1584.2.cd.c		16
99.m	even	15	1		1089.2.d.g		16
99.n	odd	30	1		1089.2.d.g		16
99.o	odd	30	1		99.2.j.a	✓	16
99.o	odd	30	1	inner	891.2.u.c		32
99.o	odd	30	1		1089.2.d.g		16
99.p	even	30	1		99.2.j.a	✓	16
99.p	even	30	1	inner	891.2.u.c		32
99.p	even	30	1		1089.2.d.g		16
396.bb	odd	30	1		1584.2.cd.c		16
396.bf	even	30	1		1584.2.cd.c		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
99.2.j.a	✓	16	9.c	even	3	1
99.2.j.a	✓	16	9.d	odd	6	1
99.2.j.a	✓	16	99.o	odd	30	1
99.2.j.a	✓	16	99.p	even	30	1
891.2.u.c		32	1.a	even	1	1	trivial
891.2.u.c		32	3.b	odd	2	1	inner
891.2.u.c		32	9.c	even	3	1	inner
891.2.u.c		32	9.d	odd	6	1	inner
891.2.u.c		32	11.d	odd	10	1	inner
891.2.u.c		32	33.f	even	10	1	inner
891.2.u.c		32	99.o	odd	30	1	inner
891.2.u.c		32	99.p	even	30	1	inner
1089.2.d.g		16	99.m	even	15	1
1089.2.d.g		16	99.n	odd	30	1
1089.2.d.g		16	99.o	odd	30	1
1089.2.d.g		16	99.p	even	30	1
1584.2.cd.c		16	36.f	odd	6	1
1584.2.cd.c		16	36.h	even	6	1
1584.2.cd.c		16	396.bb	odd	30	1
1584.2.cd.c		16	396.bf	even	30	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 6*T2^30 - T2^28 + 234*T2^26 - 1229*T2^24 + 5502*T2^22 + 1966*T2^20 - 220878*T2^18 + 1317567*T2^16 - 914172*T2^14 + 416366*T2^12 - 189252*T2^10 + 48646*T2^8 + 2916*T2^6 - 176*T2^4 + 6*T2^2 + 1