Newform orbit 2646.2.t.c

• Label: 2646.2.t.c
• Level: $2646$
• Weight: $2$
• Character orbit: 2646.t
• Analytic conductor: $21.128$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(21.1284163748\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 882)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 24 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1979.1	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−1.44900				0			0				1.00000i		0		1.25487	−	0.724499i
1979.2	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	1.44900				0			0				1.00000i		0		−1.25487	+	0.724499i
1979.3	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−1.42597				0			0				1.00000i		0		1.23492	−	0.712984i
1979.4	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	1.42597				0			0				1.00000i		0		−1.23492	+	0.712984i
1979.5	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−1.16972				0			0				1.00000i		0		1.01301	−	0.584859i
1979.6	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	1.16972				0			0				1.00000i		0		−1.01301	+	0.584859i
1979.7	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−0.949113				0			0				1.00000i		0		0.821956	−	0.474556i
1979.8	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	0.949113				0			0				1.00000i		0		−0.821956	+	0.474556i
1979.9	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−2.70053				0			0				1.00000i		0		2.33872	−	1.35026i
1979.10	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	2.70053				0			0				1.00000i		0		−2.33872	+	1.35026i
1979.11	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	−3.92134				0			0				1.00000i		0		3.39598	−	1.96067i
1979.12	−0.866025	+	0.500000i		0		0.500000	−	0.866025i	3.92134				0			0				1.00000i		0		−3.39598	+	1.96067i
1979.13	0.866025	−	0.500000i		0		0.500000	−	0.866025i	−3.98682				0			0			−	1.00000i		0		−3.45268	+	1.99341i
1979.14	0.866025	−	0.500000i		0		0.500000	−	0.866025i	3.98682				0			0			−	1.00000i		0		3.45268	−	1.99341i
1979.15	0.866025	−	0.500000i		0		0.500000	−	0.866025i	−0.440174				0			0			−	1.00000i		0		−0.381202	+	0.220087i
1979.16	0.866025	−	0.500000i		0		0.500000	−	0.866025i	0.440174				0			0			−	1.00000i		0		0.381202	−	0.220087i
1979.17	0.866025	−	0.500000i		0		0.500000	−	0.866025i	−1.89776				0			0			−	1.00000i		0		−1.64351	+	0.948881i
1979.18	0.866025	−	0.500000i		0		0.500000	−	0.866025i	1.89776				0			0			−	1.00000i		0		1.64351	−	0.948881i
1979.19	0.866025	−	0.500000i		0		0.500000	−	0.866025i	−1.99040				0			0			−	1.00000i		0		−1.72374	+	0.995200i
1979.20	0.866025	−	0.500000i		0		0.500000	−	0.866025i	1.99040				0			0			−	1.00000i		0		1.72374	−	0.995200i

Inner twists

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

Twists

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

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 - 72*T5^22 + 2208*T5^20 - 37880*T5^18 + 402114*T5^16 - 2762952*T5^14 + 12512864*T5^12 - 37377144*T5^10 + 72497985*T5^8 - 87971200*T5^6 + 61964352*T5^4 - 21613056*T5^2 + 2408704