Newform orbit 880.2.cm.a

• Label: 880.2.cm.a
• Level: $880$
• Weight: $2$
• Character orbit: 880.cm
• Analytic conductor: $7.027$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.02683537787\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(4\) over \(\Q(\zeta_{20})\)
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 4 q^{3} - 2 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0		−1.98021	+	0.313634i		0		−0.867371	−	2.06099i		0		−0.282837	+	1.78576i		0		0.969677	−	0.315067i		0
17.2		0		−0.760272	+	0.120415i		0		2.23511	−	0.0653109i		0		0.186656	−	1.17850i		0		−2.28966	+	0.743954i		0
17.3		0		0.822224	−	0.130227i		0		−0.233059	+	2.22389i		0		−0.659422	+	4.16343i		0		−2.19408	+	0.712899i		0
17.4		0		2.78152	−	0.440550i		0		−1.77672	−	1.35766i		0		−0.0860119	+	0.543058i		0		4.68963	−	1.52375i		0
193.1		0		−0.313634	−	1.98021i		0		1.91314	−	1.15755i		0		1.78576	+	0.282837i		0		−0.969677	+	0.315067i		0
193.2		0		−0.120415	−	0.760272i		0		−1.76986	−	1.36660i		0		−1.17850	−	0.186656i		0		2.28966	−	0.743954i		0
193.3		0		0.130227	+	0.822224i		0		−1.11862	+	1.93615i		0		4.16343	+	0.659422i		0		2.19408	−	0.712899i		0
193.4		0		0.440550	+	2.78152i		0		2.23541	−	0.0540419i		0		0.543058	+	0.0860119i		0		−4.68963	+	1.52375i		0
337.1		0		−1.15501	−	2.26684i		0		−2.23029	−	0.160637i		0		−3.09022	−	1.57455i		0		−2.04114	+	2.80938i		0
337.2		0		−0.517260	−	1.01518i		0		2.05331	−	0.885381i		0		2.59854	+	1.32402i		0		1.00032	−	1.37683i		0
337.3		0		0.271495	+	0.532840i		0		1.85044	+	1.25533i		0		−2.30033	−	1.17208i		0		1.55315	−	2.13772i		0
337.4		0		0.361933	+	0.710333i		0		−1.89470	+	1.18749i		0		−0.170602	−	0.0869260i		0		1.38978	−	1.91287i		0
497.1		0		−0.313634	+	1.98021i		0		1.91314	+	1.15755i		0		1.78576	−	0.282837i		0		−0.969677	−	0.315067i		0
497.2		0		−0.120415	+	0.760272i		0		−1.76986	+	1.36660i		0		−1.17850	+	0.186656i		0		2.28966	+	0.743954i		0
497.3		0		0.130227	−	0.822224i		0		−1.11862	−	1.93615i		0		4.16343	−	0.659422i		0		2.19408	+	0.712899i		0
497.4		0		0.440550	−	2.78152i		0		2.23541	+	0.0540419i		0		0.543058	−	0.0860119i		0		−4.68963	−	1.52375i		0
513.1		0		−0.710333	+	0.361933i		0		−1.71486	+	1.43501i		0		−0.0869260	+	0.170602i		0		−1.38978	+	1.91287i		0
513.2		0		−0.532840	+	0.271495i		0		−0.622076	−	2.14779i		0		−1.17208	+	2.30033i		0		−1.55315	+	2.13772i		0
513.3		0		1.01518	−	0.517260i		0		1.47656	−	1.67922i		0		1.32402	−	2.59854i		0		−1.00032	+	1.37683i		0
513.4		0		2.26684	−	1.15501i		0		−0.536423	+	2.17077i		0		−1.57455	+	3.09022i		0		2.04114	−	2.80938i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.d	odd	10	1	inner
55.l	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	880.2.cm.a		32
4.b	odd	2	1		55.2.l.a	✓	32
5.c	odd	4	1	inner	880.2.cm.a		32
11.d	odd	10	1	inner	880.2.cm.a		32
12.b	even	2	1		495.2.bj.a		32
20.d	odd	2	1		275.2.bm.b		32
20.e	even	4	1		55.2.l.a	✓	32
20.e	even	4	1		275.2.bm.b		32
44.c	even	2	1		605.2.m.e		32
44.g	even	10	1		55.2.l.a	✓	32
44.g	even	10	1		605.2.e.b		32
44.g	even	10	1		605.2.m.c		32
44.g	even	10	1		605.2.m.d		32
44.h	odd	10	1		605.2.e.b		32
44.h	odd	10	1		605.2.m.c		32
44.h	odd	10	1		605.2.m.d		32
44.h	odd	10	1		605.2.m.e		32
55.l	even	20	1	inner	880.2.cm.a		32
60.l	odd	4	1		495.2.bj.a		32
132.n	odd	10	1		495.2.bj.a		32
220.i	odd	4	1		605.2.m.e		32
220.o	even	10	1		275.2.bm.b		32
220.v	even	20	1		605.2.e.b		32
220.v	even	20	1		605.2.m.c		32
220.v	even	20	1		605.2.m.d		32
220.v	even	20	1		605.2.m.e		32
220.w	odd	20	1		55.2.l.a	✓	32
220.w	odd	20	1		275.2.bm.b		32
220.w	odd	20	1		605.2.e.b		32
220.w	odd	20	1		605.2.m.c		32
220.w	odd	20	1		605.2.m.d		32
660.bv	even	20	1		495.2.bj.a		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.2.l.a	✓	32	4.b	odd	2	1
55.2.l.a	✓	32	20.e	even	4	1
55.2.l.a	✓	32	44.g	even	10	1
55.2.l.a	✓	32	220.w	odd	20	1
275.2.bm.b		32	20.d	odd	2	1
275.2.bm.b		32	20.e	even	4	1
275.2.bm.b		32	220.o	even	10	1
275.2.bm.b		32	220.w	odd	20	1
495.2.bj.a		32	12.b	even	2	1
495.2.bj.a		32	60.l	odd	4	1
495.2.bj.a		32	132.n	odd	10	1
495.2.bj.a		32	660.bv	even	20	1
605.2.e.b		32	44.g	even	10	1
605.2.e.b		32	44.h	odd	10	1
605.2.e.b		32	220.v	even	20	1
605.2.e.b		32	220.w	odd	20	1
605.2.m.c		32	44.g	even	10	1
605.2.m.c		32	44.h	odd	10	1
605.2.m.c		32	220.v	even	20	1
605.2.m.c		32	220.w	odd	20	1
605.2.m.d		32	44.g	even	10	1
605.2.m.d		32	44.h	odd	10	1
605.2.m.d		32	220.v	even	20	1
605.2.m.d		32	220.w	odd	20	1
605.2.m.e		32	44.c	even	2	1
605.2.m.e		32	44.h	odd	10	1
605.2.m.e		32	220.i	odd	4	1
605.2.m.e		32	220.v	even	20	1
880.2.cm.a		32	1.a	even	1	1	trivial
880.2.cm.a		32	5.c	odd	4	1	inner
880.2.cm.a		32	11.d	odd	10	1	inner
880.2.cm.a		32	55.l	even	20	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^32 - 4*T3^31 + 8*T3^30 - 28*T3^29 + 29*T3^28 + 36*T3^27 + 16*T3^26 + 858*T3^25 - 2328*T3^24 - 1156*T3^23 - 592*T3^22 + 788*T3^21 + 43959*T3^20 + 1836*T3^19 - 198*T3^18 - 27498*T3^17 - 4833*T3^16 + 33116*T3^15 + 10734*T3^14 + 32308*T3^13 + 33159*T3^12 - 11726*T3^11 - 7218*T3^10 - 9302*T3^9 - 21604*T3^8 - 5770*T3^7 - 300*T3^6 + 50*T3^5 + 5825*T3^4 + 3750*T3^3 + 1250*T3^2 + 1250*T3 + 625