Newform orbit 1050.3.q.e

• Label: 1050.3.q.e
• Level: $1050$
• Weight: $3$
• Character orbit: 1050.q
• Analytic conductor: $28.610$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.6104277578\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 210)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
199.1	−1.22474	+	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	−2.86123	−	6.38854i			2.82843i	−1.50000	−	2.59808i		0
199.2	−1.22474	+	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0				2.44949i	4.01037	−	5.73733i			2.82843i	−1.50000	−	2.59808i		0
199.3	−1.22474	+	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0				2.44949i	−6.50174	+	2.59373i			2.82843i	−1.50000	−	2.59808i		0
199.4	−1.22474	+	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0				2.44949i	−6.72455	−	1.94434i			2.82843i	−1.50000	−	2.59808i		0
199.5	−1.22474	+	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	5.56601	+	4.24494i			2.82843i	−1.50000	−	2.59808i		0
199.6	−1.22474	+	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0				2.44949i	6.46925	+	2.67372i			2.82843i	−1.50000	−	2.59808i		0
199.7	−1.22474	+	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	4.61524	−	5.26304i			2.82843i	−1.50000	−	2.59808i		0
199.8	−1.22474	+	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	0.325616	+	6.99242i			2.82843i	−1.50000	−	2.59808i		0
199.9	1.22474	−	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	−0.325616	−	6.99242i		−	2.82843i	−1.50000	−	2.59808i		0
199.10	1.22474	−	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	2.86123	+	6.38854i		−	2.82843i	−1.50000	−	2.59808i		0
199.11	1.22474	−	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	−5.56601	−	4.24494i		−	2.82843i	−1.50000	−	2.59808i		0
199.12	1.22474	−	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0				2.44949i	6.72455	+	1.94434i		−	2.82843i	−1.50000	−	2.59808i		0
199.13	1.22474	−	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0				2.44949i	−6.46925	−	2.67372i		−	2.82843i	−1.50000	−	2.59808i		0
199.14	1.22474	−	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0				2.44949i	6.50174	−	2.59373i		−	2.82843i	−1.50000	−	2.59808i		0
199.15	1.22474	−	0.707107i	−0.866025	+	1.50000i	1.00000	−	1.73205i		0				2.44949i	−4.01037	+	5.73733i		−	2.82843i	−1.50000	−	2.59808i		0
199.16	1.22474	−	0.707107i	0.866025	−	1.50000i	1.00000	−	1.73205i		0			−	2.44949i	−4.61524	+	5.26304i		−	2.82843i	−1.50000	−	2.59808i		0
649.1	−1.22474	−	0.707107i	−0.866025	−	1.50000i	1.00000	+	1.73205i		0				2.44949i	−2.86123	+	6.38854i		−	2.82843i	−1.50000	+	2.59808i		0
649.2	−1.22474	−	0.707107i	0.866025	+	1.50000i	1.00000	+	1.73205i		0			−	2.44949i	4.01037	+	5.73733i		−	2.82843i	−1.50000	+	2.59808i		0
649.3	−1.22474	−	0.707107i	0.866025	+	1.50000i	1.00000	+	1.73205i		0			−	2.44949i	−6.50174	−	2.59373i		−	2.82843i	−1.50000	+	2.59808i		0
649.4	−1.22474	−	0.707107i	0.866025	+	1.50000i	1.00000	+	1.73205i		0			−	2.44949i	−6.72455	+	1.94434i		−	2.82843i	−1.50000	+	2.59808i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.d	odd	6	1	inner
35.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1050.3.q.e		32
5.b	even	2	1	inner	1050.3.q.e		32
5.c	odd	4	1		210.3.o.b	✓	16
5.c	odd	4	1		1050.3.p.i		16
7.d	odd	6	1	inner	1050.3.q.e		32
15.e	even	4	1		630.3.v.c		16
35.i	odd	6	1	inner	1050.3.q.e		32
35.k	even	12	1		210.3.o.b	✓	16
35.k	even	12	1		1050.3.p.i		16
35.k	even	12	1		1470.3.f.d		16
35.l	odd	12	1		1470.3.f.d		16
105.w	odd	12	1		630.3.v.c		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.3.o.b	✓	16	5.c	odd	4	1
210.3.o.b	✓	16	35.k	even	12	1
630.3.v.c		16	15.e	even	4	1
630.3.v.c		16	105.w	odd	12	1
1050.3.p.i		16	5.c	odd	4	1
1050.3.p.i		16	35.k	even	12	1
1050.3.q.e		32	1.a	even	1	1	trivial
1050.3.q.e		32	5.b	even	2	1	inner
1050.3.q.e		32	7.d	odd	6	1	inner
1050.3.q.e		32	35.i	odd	6	1	inner
1470.3.f.d		16	35.k	even	12	1
1470.3.f.d		16	35.l	odd	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^16 + 4*T11^15 + 604*T11^14 + 352*T11^13 + 252064*T11^12 + 129616*T11^11 + 49322848*T11^10 - 7989152*T11^9 + 6945139504*T11^8 + 676772544*T11^7 + 516442695552*T11^6 - 11416664448*T11^5 + 26420738609664*T11^4 + 15929692886016*T11^3 + 26588869767936*T11^2 - 10143730662912*T11 + 9682651996416