Newform orbit 756.2.ck.a

• Label: 756.2.ck.a
• Level: $756$
• Weight: $2$
• Character orbit: 756.ck
• Analytic conductor: $6.037$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.03669039281\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(24\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1		0		−1.70107	−	0.326131i		0		−0.752649	+	4.26848i		0		−2.02371	−	1.70429i		0		2.78728	+	1.10954i		0
5.2		0		−1.69135	+	0.373296i		0		−0.203680	+	1.15512i		0		2.02312	+	1.70498i		0		2.72130	−	1.26275i		0
5.3		0		−1.63320	+	0.576754i		0		0.109190	−	0.619249i		0		−2.49443	+	0.881937i		0		2.33471	−	1.88391i		0
5.4		0		−1.63242	+	0.578955i		0		0.649280	−	3.68225i		0		0.647047	−	2.56541i		0		2.32962	−	1.89020i		0
5.5		0		−1.61581	−	0.623825i		0		−0.221654	+	1.25706i		0		2.55927	−	0.670941i		0		2.22168	+	2.01597i		0
5.6		0		−1.47292	−	0.911314i		0		0.688949	−	3.90722i		0		0.608733	+	2.57477i		0		1.33902	+	2.68459i		0
5.7		0		−1.33105	−	1.10829i		0		0.180656	−	1.02455i		0		−1.77393	−	1.96295i		0		0.543390	+	2.95038i		0
5.8		0		−0.792956	+	1.53988i		0		−0.192493	+	1.09168i		0		−0.137506	−	2.64218i		0		−1.74244	−	2.44211i		0
5.9		0		−0.573178	−	1.63446i		0		−0.0962103	+	0.545636i		0		2.05240	−	1.66962i		0		−2.34293	+	1.87368i		0
5.10		0		−0.538039	+	1.64636i		0		−0.430811	+	2.44325i		0		−0.571962	+	2.58319i		0		−2.42103	−	1.77162i		0
5.11		0		−0.230632	−	1.71663i		0		0.315692	−	1.79038i		0		0.645961	+	2.56568i		0		−2.89362	+	0.791819i		0
5.12		0		−0.0439893	−	1.73149i		0		−0.310888	+	1.76313i		0		−1.91547	+	1.82510i		0		−2.99613	+	0.152334i		0
5.13		0		0.212510	+	1.71896i		0		0.455707	−	2.58444i		0		2.64406	−	0.0947211i		0		−2.90968	+	0.730593i		0
5.14		0		0.277790	+	1.70963i		0		0.630118	−	3.57358i		0		−2.41159	+	1.08823i		0		−2.84567	+	0.949836i		0
5.15		0		0.671662	+	1.59652i		0		−0.158784	+	0.900507i		0		−0.241705	−	2.63469i		0		−2.09774	+	2.14464i		0
5.16		0		0.727904	−	1.57167i		0		−0.591212	+	3.35293i		0		−1.25160	−	2.33098i		0		−1.94031	−	2.28805i		0
5.17		0		1.06196	−	1.36830i		0		0.449866	−	2.55131i		0		−2.53584	−	0.754675i		0		−0.744465	−	2.90616i		0
5.18		0		1.11789	+	1.32299i		0		−0.682386	+	3.87000i		0		2.62129	+	0.358920i		0		−0.500623	+	2.95793i		0
5.19		0		1.26963	+	1.17815i		0		0.263400	−	1.49382i		0		0.0912000	+	2.64418i		0		0.223916	+	2.99163i		0
5.20		0		1.37168	−	1.05759i		0		−0.403931	+	2.29081i		0		2.60966	+	0.435529i		0		0.762996	−	2.90135i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
189.ba	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	756.2.ck.a	yes	144
7.d	odd	6	1		756.2.ca.a	✓	144
27.f	odd	18	1		756.2.ca.a	✓	144
189.ba	even	18	1	inner	756.2.ck.a	yes	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
756.2.ca.a	✓	144	7.d	odd	6	1
756.2.ca.a	✓	144	27.f	odd	18	1
756.2.ck.a	yes	144	1.a	even	1	1	trivial
756.2.ck.a	yes	144	189.ba	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(756, [\chi])\).