Newform orbit 945.2.bb.c

• Label: 945.2.bb.c
• Level: $945$
• Weight: $2$
• Character orbit: 945.bb
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 32 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
269.1	−1.38892	−	2.40568i		0		−2.85820	+	4.95055i	−2.06628	−	0.854682i		0		2.56681	−	0.641452i	10.3236				0		0.813807	+	6.15790i
269.2	−1.38892	−	2.40568i		0		−2.85820	+	4.95055i	−0.292964	+	2.21679i		0		−2.56681	+	0.641452i	10.3236				0		5.73980	−	2.37417i
269.3	−1.09348	−	1.89395i		0		−1.39138	+	2.40993i	−0.218229	−	2.22539i		0		−0.137765	+	2.64216i	1.71184				0		−3.97617	+	2.84673i
269.4	−1.09348	−	1.89395i		0		−1.39138	+	2.40993i	1.81813	+	1.30169i		0		0.137765	−	2.64216i	1.71184				0		0.477256	−	4.86683i
269.5	−1.03521	−	1.79303i		0		−1.14331	+	1.98027i	0.419919	−	2.19629i		0		−2.18996	−	1.48461i	0.593416				0		−4.37271	+	1.52068i
269.6	−1.03521	−	1.79303i		0		−1.14331	+	1.98027i	2.11200	+	0.734482i		0		2.18996	+	1.48461i	0.593416				0		−0.869406	−	4.54722i
269.7	−0.975951	−	1.69040i		0		−0.904961	+	1.56744i	−2.17635	+	0.513320i		0		2.05933	−	1.66107i	−0.371013				0		2.99173	+	3.17792i
269.8	−0.975951	−	1.69040i		0		−0.904961	+	1.56744i	−1.53272	+	1.62811i		0		−2.05933	+	1.66107i	−0.371013				0		4.24802	+	1.00195i
269.9	−0.699059	−	1.21081i		0		0.0226319	−	0.0391995i	−0.911294	−	2.04195i		0		2.09455	+	1.61644i	−2.85952				0		−1.83535	+	2.53084i
269.10	−0.699059	−	1.21081i		0		0.0226319	−	0.0391995i	1.31273	+	1.81018i		0		−2.09455	−	1.61644i	−2.85952				0		1.27410	−	2.85488i
269.11	−0.447113	−	0.774423i		0		0.600180	−	1.03954i	1.85694	−	1.24570i		0		−2.64288	+	0.123314i	−2.86185				0		−1.79496	−	0.881090i
269.12	−0.447113	−	0.774423i		0		0.600180	−	1.03954i	2.00728	−	0.985310i		0		2.64288	−	0.123314i	−2.86185				0		−1.66053	−	1.11394i
269.13	−0.326083	−	0.564792i		0		0.787340	−	1.36371i	−2.21234	+	0.324872i		0		−1.27963	−	2.31572i	−2.33128				0		0.904891	+	1.14358i
269.14	−0.326083	−	0.564792i		0		0.787340	−	1.36371i	−1.38752	+	1.75351i		0		1.27963	+	2.31572i	−2.33128				0		1.44281	+	0.211870i
269.15	−0.236963	−	0.410432i		0		0.887697	−	1.53754i	−0.689007	−	2.12727i		0		1.04705	−	2.42975i	−1.78926				0		−0.709829	+	0.786874i
269.16	−0.236963	−	0.410432i		0		0.887697	−	1.53754i	1.49776	+	1.66033i		0		−1.04705	+	2.42975i	−1.78926				0		0.326538	−	1.00817i
269.17	0.236963	+	0.410432i		0		0.887697	−	1.53754i	−1.49776	−	1.66033i		0		−1.04705	+	2.42975i	1.78926				0		0.326538	−	1.00817i
269.18	0.236963	+	0.410432i		0		0.887697	−	1.53754i	0.689007	+	2.12727i		0		1.04705	−	2.42975i	1.78926				0		−0.709829	+	0.786874i
269.19	0.326083	+	0.564792i		0		0.787340	−	1.36371i	1.38752	−	1.75351i		0		1.27963	+	2.31572i	2.33128				0		1.44281	+	0.211870i
269.20	0.326083	+	0.564792i		0		0.787340	−	1.36371i	2.21234	−	0.324872i		0		−1.27963	−	2.31572i	2.33128				0		0.904891	+	1.14358i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
7.d	odd	6	1	inner
15.d	odd	2	1	inner
21.g	even	6	1	inner
35.i	odd	6	1	inner
105.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.bb.c	✓	64
3.b	odd	2	1	inner	945.2.bb.c	✓	64
5.b	even	2	1	inner	945.2.bb.c	✓	64
7.d	odd	6	1	inner	945.2.bb.c	✓	64
15.d	odd	2	1	inner	945.2.bb.c	✓	64
21.g	even	6	1	inner	945.2.bb.c	✓	64
35.i	odd	6	1	inner	945.2.bb.c	✓	64
105.p	even	6	1	inner	945.2.bb.c	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.bb.c	✓	64	1.a	even	1	1	trivial
945.2.bb.c	✓	64	3.b	odd	2	1	inner
945.2.bb.c	✓	64	5.b	even	2	1	inner
945.2.bb.c	✓	64	7.d	odd	6	1	inner
945.2.bb.c	✓	64	15.d	odd	2	1	inner
945.2.bb.c	✓	64	21.g	even	6	1	inner
945.2.bb.c	✓	64	35.i	odd	6	1	inner
945.2.bb.c	✓	64	105.p	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 + 24*T2^30 + 348*T2^28 + 3270*T2^26 + 22686*T2^24 + 117063*T2^22 + 466731*T2^20 + 1412928*T2^18 + 3284847*T2^16 + 5609196*T2^14 + 7116633*T2^12 + 6180597*T2^10 + 3903363*T2^8 + 1604610*T2^6 + 468666*T2^4 + 76140*T2^2 + 8100