Newform orbit 1260.2.dq.c

• Label: 1260.2.dq.c
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.dq
• Analytic conductor: $10.061$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.dq (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.0611506547\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 12 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
73.1		0			0			0		−2.22732	−	0.197620i		0		2.20765	−	1.45817i		0			0			0
73.2		0			0			0		−1.40421	−	1.74017i		0		1.06666	+	2.42120i		0			0			0
73.3		0			0			0		−0.541965	+	2.16939i		0		2.42432	−	1.05955i		0			0			0
73.4		0			0			0		0.0833091	−	2.23452i		0		−1.70817	+	2.02043i		0			0			0
73.5		0			0			0		1.25559	+	1.85027i		0		−2.64359	−	0.106918i		0			0			0
73.6		0			0			0		1.57194	−	1.59028i		0		−1.62725	−	2.08616i		0			0			0
73.7		0			0			0		2.12960	+	0.681768i		0		1.94431	+	1.79435i		0			0			0
73.8		0			0			0		2.13305	−	0.670893i		0		1.80016	+	1.93892i		0			0			0
397.1		0			0			0		−2.22732	+	0.197620i		0		2.20765	+	1.45817i		0			0			0
397.2		0			0			0		−1.40421	+	1.74017i		0		1.06666	−	2.42120i		0			0			0
397.3		0			0			0		−0.541965	−	2.16939i		0		2.42432	+	1.05955i		0			0			0
397.4		0			0			0		0.0833091	+	2.23452i		0		−1.70817	−	2.02043i		0			0			0
397.5		0			0			0		1.25559	−	1.85027i		0		−2.64359	+	0.106918i		0			0			0
397.6		0			0			0		1.57194	+	1.59028i		0		−1.62725	+	2.08616i		0			0			0
397.7		0			0			0		2.12960	−	0.681768i		0		1.94431	−	1.79435i		0			0			0
397.8		0			0			0		2.13305	+	0.670893i		0		1.80016	−	1.93892i		0			0			0
577.1		0			0			0		−2.14973	−	0.615342i		0		1.05955	+	2.42432i		0			0			0
577.2		0			0			0		−0.974584	−	2.01251i		0		0.106918	−	2.64359i		0			0			0
577.3		0			0			0		−0.942515	+	2.02772i		0		1.45817	+	2.20765i		0			0			0
577.4		0			0			0		0.474372	−	2.18517i		0		−1.79435	+	1.94431i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.d	odd	6	1	inner
35.k	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1260.2.dq.c		32
3.b	odd	2	1		420.2.bo.a	✓	32
5.c	odd	4	1	inner	1260.2.dq.c		32
7.d	odd	6	1	inner	1260.2.dq.c		32
15.d	odd	2	1		2100.2.ce.e		32
15.e	even	4	1		420.2.bo.a	✓	32
15.e	even	4	1		2100.2.ce.e		32
21.g	even	6	1		420.2.bo.a	✓	32
21.g	even	6	1		2940.2.x.c		32
21.h	odd	6	1		2940.2.x.c		32
35.k	even	12	1	inner	1260.2.dq.c		32
105.p	even	6	1		2100.2.ce.e		32
105.w	odd	12	1		420.2.bo.a	✓	32
105.w	odd	12	1		2100.2.ce.e		32
105.w	odd	12	1		2940.2.x.c		32
105.x	even	12	1		2940.2.x.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
420.2.bo.a	✓	32	3.b	odd	2	1
420.2.bo.a	✓	32	15.e	even	4	1
420.2.bo.a	✓	32	21.g	even	6	1
420.2.bo.a	✓	32	105.w	odd	12	1
1260.2.dq.c		32	1.a	even	1	1	trivial
1260.2.dq.c		32	5.c	odd	4	1	inner
1260.2.dq.c		32	7.d	odd	6	1	inner
1260.2.dq.c		32	35.k	even	12	1	inner
2100.2.ce.e		32	15.d	odd	2	1
2100.2.ce.e		32	15.e	even	4	1
2100.2.ce.e		32	105.p	even	6	1
2100.2.ce.e		32	105.w	odd	12	1
2940.2.x.c		32	21.g	even	6	1
2940.2.x.c		32	21.h	odd	6	1
2940.2.x.c		32	105.w	odd	12	1
2940.2.x.c		32	105.x	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^16 + 4*T11^15 + 70*T11^14 + 168*T11^13 + 2898*T11^12 + 6448*T11^11 + 64752*T11^10 + 86004*T11^9 + 869734*T11^8 + 1337440*T11^7 + 6356356*T11^6 + 8329424*T11^5 + 29979024*T11^4 + 40152600*T11^3 + 65259740*T11^2 + 33167800*T11 + 14668900