Newform orbit 968.2.o.c

• Label: 968.2.o.c
• Level: $968$
• Weight: $2$
• Character orbit: 968.o
• Analytic conductor: $7.730$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $16$

Newspace parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.72951891566\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 8 q^{4} + 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
245.1	−1.40928	−	0.118079i	−2.66099	+	0.864609i	1.97211	+	0.332813i	−0.681209	+	0.937603i	3.85216	−	0.904264i	−0.935846	+	2.88024i	−2.73995	−	0.701891i	3.90628	−	2.83808i	1.07072	−	1.24090i
245.2	−1.32637	+	0.490644i	1.40150	−	0.455375i	1.51854	−	1.30156i	−2.09113	+	2.87820i	−1.63549	+	1.29164i	1.18995	−	3.66230i	−1.37555	+	2.47141i	−0.670212	+	0.486937i	1.36145	−	4.84357i
245.3	−0.876503	+	1.10984i	−1.40150	+	0.455375i	−0.463486	−	1.94555i	2.09113	−	2.87820i	0.723026	−	1.95458i	1.18995	−	3.66230i	2.56550	+	1.19089i	−0.670212	+	0.486937i	1.36145	+	4.84357i
245.4	−0.323190	+	1.37679i	2.66099	−	0.864609i	−1.79110	−	0.889929i	0.681209	−	0.937603i	0.330378	+	3.94306i	−0.935846	+	2.88024i	1.80411	−	2.17835i	3.90628	−	2.83808i	1.07072	+	1.24090i
245.5	0.323190	−	1.37679i	2.66099	−	0.864609i	−1.79110	−	0.889929i	0.681209	−	0.937603i	−0.330378	−	3.94306i	0.935846	−	2.88024i	−1.80411	+	2.17835i	3.90628	−	2.83808i	−1.07072	−	1.24090i
245.6	0.876503	−	1.10984i	−1.40150	+	0.455375i	−0.463486	−	1.94555i	2.09113	−	2.87820i	−0.723026	+	1.95458i	−1.18995	+	3.66230i	−2.56550	−	1.19089i	−0.670212	+	0.486937i	−1.36145	−	4.84357i
245.7	1.32637	−	0.490644i	1.40150	−	0.455375i	1.51854	−	1.30156i	−2.09113	+	2.87820i	1.63549	−	1.29164i	−1.18995	+	3.66230i	1.37555	−	2.47141i	−0.670212	+	0.486937i	−1.36145	+	4.84357i
245.8	1.40928	+	0.118079i	−2.66099	+	0.864609i	1.97211	+	0.332813i	−0.681209	+	0.937603i	−3.85216	+	0.904264i	0.935846	−	2.88024i	2.73995	+	0.701891i	3.90628	−	2.83808i	−1.07072	+	1.24090i
269.1	−1.20953	−	0.732823i	−1.64458	+	2.26358i	0.925941	+	1.77275i	1.10222	+	0.358133i	3.64798	−	1.53268i	−2.45008	+	1.78008i	0.179155	−	2.82275i	−1.49207	−	4.59211i	−1.07072	−	1.24090i
269.2	−0.784666	−	1.17656i	0.866175	−	1.19219i	−0.768600	+	1.84642i	3.38352	+	1.09937i	−2.08234	−	0.0836407i	3.11534	−	2.26343i	2.77552	−	0.544514i	0.255998	+	0.787881i	−1.36145	−	4.84357i
269.3	−0.547790	+	1.30381i	1.64458	−	2.26358i	−1.39985	−	1.42843i	−1.10222	−	0.358133i	2.05039	+	3.38419i	2.45008	−	1.78008i	2.62923	−	1.04266i	−1.49207	−	4.59211i	1.07072	−	1.24090i
269.4	−0.0567584	−	1.41307i	−0.866175	+	1.19219i	−1.99356	+	0.160408i	−3.38352	−	1.09937i	1.73381	+	1.15630i	3.11534	−	2.26343i	0.339819	+	2.80794i	0.255998	+	0.787881i	−1.36145	+	4.84357i
269.5	0.0567584	+	1.41307i	−0.866175	+	1.19219i	−1.99356	+	0.160408i	−3.38352	−	1.09937i	−1.73381	−	1.15630i	−3.11534	+	2.26343i	−0.339819	−	2.80794i	0.255998	+	0.787881i	1.36145	−	4.84357i
269.6	0.547790	−	1.30381i	1.64458	−	2.26358i	−1.39985	−	1.42843i	−1.10222	−	0.358133i	−2.05039	−	3.38419i	−2.45008	+	1.78008i	−2.62923	+	1.04266i	−1.49207	−	4.59211i	−1.07072	+	1.24090i
269.7	0.784666	+	1.17656i	0.866175	−	1.19219i	−0.768600	+	1.84642i	3.38352	+	1.09937i	2.08234	+	0.0836407i	−3.11534	+	2.26343i	−2.77552	+	0.544514i	0.255998	+	0.787881i	1.36145	+	4.84357i
269.8	1.20953	+	0.732823i	−1.64458	+	2.26358i	0.925941	+	1.77275i	1.10222	+	0.358133i	−3.64798	+	1.53268i	2.45008	−	1.78008i	−0.179155	+	2.82275i	−1.49207	−	4.59211i	1.07072	+	1.24090i
493.1	−1.20953	+	0.732823i	−1.64458	−	2.26358i	0.925941	−	1.77275i	1.10222	−	0.358133i	3.64798	+	1.53268i	−2.45008	−	1.78008i	0.179155	+	2.82275i	−1.49207	+	4.59211i	−1.07072	+	1.24090i
493.2	−0.784666	+	1.17656i	0.866175	+	1.19219i	−0.768600	−	1.84642i	3.38352	−	1.09937i	−2.08234	+	0.0836407i	3.11534	+	2.26343i	2.77552	+	0.544514i	0.255998	−	0.787881i	−1.36145	+	4.84357i
493.3	−0.547790	−	1.30381i	1.64458	+	2.26358i	−1.39985	+	1.42843i	−1.10222	+	0.358133i	2.05039	−	3.38419i	2.45008	+	1.78008i	2.62923	+	1.04266i	−1.49207	+	4.59211i	1.07072	+	1.24090i
493.4	−0.0567584	+	1.41307i	−0.866175	−	1.19219i	−1.99356	−	0.160408i	−3.38352	+	1.09937i	1.73381	−	1.15630i	3.11534	+	2.26343i	0.339819	−	2.80794i	0.255998	−	0.787881i	−1.36145	−	4.84357i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
11.b	odd	2	1	inner
11.c	even	5	3	inner
11.d	odd	10	3	inner
88.b	odd	2	1	inner
88.o	even	10	3	inner
88.p	odd	10	3	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	968.2.o.c		32
8.b	even	2	1	inner	968.2.o.c		32
11.b	odd	2	1	inner	968.2.o.c		32
11.c	even	5	1		968.2.c.c	✓	8
11.c	even	5	3	inner	968.2.o.c		32
11.d	odd	10	1		968.2.c.c	✓	8
11.d	odd	10	3	inner	968.2.o.c		32
44.g	even	10	1		3872.2.c.c		8
44.h	odd	10	1		3872.2.c.c		8
88.b	odd	2	1	inner	968.2.o.c		32
88.k	even	10	1		3872.2.c.c		8
88.l	odd	10	1		3872.2.c.c		8
88.o	even	10	1		968.2.c.c	✓	8
88.o	even	10	3	inner	968.2.o.c		32
88.p	odd	10	1		968.2.c.c	✓	8
88.p	odd	10	3	inner	968.2.o.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
968.2.c.c	✓	8	11.c	even	5	1
968.2.c.c	✓	8	11.d	odd	10	1
968.2.c.c	✓	8	88.o	even	10	1
968.2.c.c	✓	8	88.p	odd	10	1
968.2.o.c		32	1.a	even	1	1	trivial
968.2.o.c		32	8.b	even	2	1	inner
968.2.o.c		32	11.b	odd	2	1	inner
968.2.o.c		32	11.c	even	5	3	inner
968.2.o.c		32	11.d	odd	10	3	inner
968.2.o.c		32	88.b	odd	2	1	inner
968.2.o.c		32	88.o	even	10	3	inner
968.2.o.c		32	88.p	odd	10	3	inner
3872.2.c.c		8	44.g	even	10	1
3872.2.c.c		8	44.h	odd	10	1
3872.2.c.c		8	88.k	even	10	1
3872.2.c.c		8	88.l	odd	10	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(968, [\chi])\):

\( T_{3}^{16} - 10T_{3}^{14} + 83T_{3}^{12} - 660T_{3}^{10} + 5189T_{3}^{8} - 11220T_{3}^{6} + 23987T_{3}^{4} - 49130T_{3}^{2} + 83521 \)

T5^16 - 14*T5^14 + 179*T5^12 - 2268*T5^10 + 28709*T5^8 - 38556*T5^6 + 51731*T5^4 - 68782*T5^2 + 83521

T7^16 + 24*T7^14 + 440*T7^12 + 7296*T7^10 + 115264*T7^8 + 992256*T7^6 + 8138240*T7^4 + 60370944*T7^2 + 342102016