Newform orbit 882.2.l.c

• Label: 882.2.l.c
• Level: $882$
• Weight: $2$
• Character orbit: 882.l
• Analytic conductor: $7.043$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.04280545828\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
227.1		−	1.00000i	−1.70306	+	0.315583i	−1.00000			0.220087	−	0.381202i	0.315583	+	1.70306i		0				1.00000i	2.80082	−	1.07491i	−0.381202	−	0.220087i
227.2		−	1.00000i	−1.63594	−	0.568941i	−1.00000			1.55389	−	2.69141i	−0.568941	+	1.63594i		0				1.00000i	2.35261	+	1.86151i	−2.69141	−	1.55389i
227.3		−	1.00000i	−1.52614	−	0.819074i	−1.00000			−1.99341	+	3.45268i	−0.819074	+	1.52614i		0				1.00000i	1.65823	+	2.50005i	3.45268	+	1.99341i
227.4		−	1.00000i	−0.495324	−	1.65972i	−1.00000			−0.995200	+	1.72374i	−1.65972	+	0.495324i		0				1.00000i	−2.50931	+	1.64419i	1.72374	+	0.995200i
227.5		−	1.00000i	−0.307440	−	1.70455i	−1.00000			1.55067	−	2.68584i	−1.70455	+	0.307440i		0				1.00000i	−2.81096	+	1.04809i	−2.68584	−	1.55067i
227.6		−	1.00000i	−0.149173	+	1.72562i	−1.00000			0.948881	−	1.64351i	1.72562	+	0.149173i		0				1.00000i	−2.95549	−	0.514831i	−1.64351	−	0.948881i
227.7		−	1.00000i	0.149173	−	1.72562i	−1.00000			−0.948881	+	1.64351i	−1.72562	−	0.149173i		0				1.00000i	−2.95549	−	0.514831i	1.64351	+	0.948881i
227.8		−	1.00000i	0.307440	+	1.70455i	−1.00000			−1.55067	+	2.68584i	1.70455	−	0.307440i		0				1.00000i	−2.81096	+	1.04809i	2.68584	+	1.55067i
227.9		−	1.00000i	0.495324	+	1.65972i	−1.00000			0.995200	−	1.72374i	1.65972	−	0.495324i		0				1.00000i	−2.50931	+	1.64419i	−1.72374	−	0.995200i
227.10		−	1.00000i	1.52614	+	0.819074i	−1.00000			1.99341	−	3.45268i	0.819074	−	1.52614i		0				1.00000i	1.65823	+	2.50005i	−3.45268	−	1.99341i
227.11		−	1.00000i	1.63594	+	0.568941i	−1.00000			−1.55389	+	2.69141i	0.568941	−	1.63594i		0				1.00000i	2.35261	+	1.86151i	2.69141	+	1.55389i
227.12		−	1.00000i	1.70306	−	0.315583i	−1.00000			−0.220087	+	0.381202i	−0.315583	−	1.70306i		0				1.00000i	2.80082	−	1.07491i	0.381202	+	0.220087i
227.13			1.00000i	−1.71914	−	0.211098i	−1.00000			0.584859	−	1.01301i	0.211098	−	1.71914i		0			−	1.00000i	2.91088	+	0.725813i	1.01301	+	0.584859i
227.14			1.00000i	−1.66366	−	0.481898i	−1.00000			−0.712984	+	1.23492i	0.481898	−	1.66366i		0			−	1.00000i	2.53555	+	1.60343i	−1.23492	−	0.712984i
227.15			1.00000i	−1.60962	−	0.639623i	−1.00000			−1.35026	+	2.33872i	0.639623	−	1.60962i		0			−	1.00000i	2.18177	+	2.05910i	−2.33872	−	1.35026i
227.16			1.00000i	−1.45331	+	0.942282i	−1.00000			0.724499	−	1.25487i	−0.942282	−	1.45331i		0			−	1.00000i	1.22421	−	2.73885i	1.25487	+	0.724499i
227.17			1.00000i	−0.848829	+	1.50980i	−1.00000			1.96067	−	3.39598i	−1.50980	−	0.848829i		0			−	1.00000i	−1.55898	−	2.56312i	3.39598	+	1.96067i
227.18			1.00000i	−0.765075	−	1.55392i	−1.00000			−0.474556	+	0.821956i	1.55392	−	0.765075i		0			−	1.00000i	−1.82932	+	2.37773i	−0.821956	−	0.474556i
227.19			1.00000i	0.765075	+	1.55392i	−1.00000			0.474556	−	0.821956i	−1.55392	+	0.765075i		0			−	1.00000i	−1.82932	+	2.37773i	0.821956	+	0.474556i
227.20			1.00000i	0.848829	−	1.50980i	−1.00000			−1.96067	+	3.39598i	1.50980	+	0.848829i		0			−	1.00000i	−1.55898	−	2.56312i	−3.39598	−	1.96067i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
63.i	even	6	1	inner
63.j	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	882.2.l.c		48
3.b	odd	2	1		2646.2.l.c		48
7.b	odd	2	1	inner	882.2.l.c		48
7.c	even	3	1		882.2.m.c	✓	48
7.c	even	3	1		882.2.t.c		48
7.d	odd	6	1		882.2.m.c	✓	48
7.d	odd	6	1		882.2.t.c		48
9.c	even	3	1		2646.2.t.c		48
9.d	odd	6	1		882.2.t.c		48
21.c	even	2	1		2646.2.l.c		48
21.g	even	6	1		2646.2.m.c		48
21.g	even	6	1		2646.2.t.c		48
21.h	odd	6	1		2646.2.m.c		48
21.h	odd	6	1		2646.2.t.c		48
63.g	even	3	1		2646.2.m.c		48
63.h	even	3	1		2646.2.l.c		48
63.i	even	6	1	inner	882.2.l.c		48
63.j	odd	6	1	inner	882.2.l.c		48
63.k	odd	6	1		2646.2.m.c		48
63.l	odd	6	1		2646.2.t.c		48
63.n	odd	6	1		882.2.m.c	✓	48
63.o	even	6	1		882.2.t.c		48
63.s	even	6	1		882.2.m.c	✓	48
63.t	odd	6	1		2646.2.l.c		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
882.2.l.c		48	1.a	even	1	1	trivial
882.2.l.c		48	7.b	odd	2	1	inner
882.2.l.c		48	63.i	even	6	1	inner
882.2.l.c		48	63.j	odd	6	1	inner
882.2.m.c	✓	48	7.c	even	3	1
882.2.m.c	✓	48	7.d	odd	6	1
882.2.m.c	✓	48	63.n	odd	6	1
882.2.m.c	✓	48	63.s	even	6	1
882.2.t.c		48	7.c	even	3	1
882.2.t.c		48	7.d	odd	6	1
882.2.t.c		48	9.d	odd	6	1
882.2.t.c		48	63.o	even	6	1
2646.2.l.c		48	3.b	odd	2	1
2646.2.l.c		48	21.c	even	2	1
2646.2.l.c		48	63.h	even	3	1
2646.2.l.c		48	63.t	odd	6	1
2646.2.m.c		48	21.g	even	6	1
2646.2.m.c		48	21.h	odd	6	1
2646.2.m.c		48	63.g	even	3	1
2646.2.m.c		48	63.k	odd	6	1
2646.2.t.c		48	9.c	even	3	1
2646.2.t.c		48	21.g	even	6	1
2646.2.t.c		48	21.h	odd	6	1
2646.2.t.c		48	63.l	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^48 + 72*T5^46 + 2976*T5^44 + 83216*T5^42 + 1745790*T5^40 + 28497576*T5^38 + 373119872*T5^36 + 3969185640*T5^34 + 34716454275*T5^32 + 250619750360*T5^30 + 1500214956096*T5^28 + 7444259677464*T5^26 + 30674385473278*T5^24 + 104704605218928*T5^22 + 295842709935840*T5^20 + 687937261293688*T5^18 + 1310957208385665*T5^16 + 2022730086777216*T5^14 + 2499086632353728*T5^12 + 2407302859539456*T5^10 + 1763628260331264*T5^8 + 915445847130112*T5^6 + 317870407139328*T5^4 + 52059454439424*T5^2 + 5801854959616