Newform orbit 627.2.l.a

• Label: 627.2.l.a
• Level: $627$
• Weight: $2$
• Character orbit: 627.l
• Analytic conductor: $5.007$
• Analytic rank: $0$
• Dimension: $152$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.00662020673\)
Analytic rank:	\(0\)
Dimension:	\(152\)
Relative dimension:	\(76\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 152 * q - 76 * q^4 - 8 * q^9 - 14 * q^15 - 76 * q^16 + 4 * q^22 + 60 * q^25 + 12 * q^27 - 16 * q^31 + 16 * q^33 - 16 * q^34 - 10 * q^36 - 16 * q^37 + 50 * q^42 - 108 * q^45 + 54 * q^48 - 80 * q^49 + 32 * q^55 - 40 * q^58 + 2 * q^60 + 152 * q^64 - 10 * q^66 - 16 * q^67 - 32 * q^69 - 4 * q^70 - 20 * q^75 - 58 * q^78 + 16 * q^81 - 40 * q^82 - 120 * q^88 - 16 * q^91 - 12 * q^93 + 4 * q^97 + 60 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
197.1	−1.40640	−	2.43595i	−0.427063	+	1.67858i	−2.95590	+	5.11976i	2.41646	−	1.39514i	4.68954	−	1.32044i		−	1.25614i	11.0031			−2.63523	−	1.43372i	−6.79700	−	3.92425i
197.2	−1.40640	−	2.43595i	1.66722	+	0.469440i	−2.95590	+	5.11976i	−2.41646	+	1.39514i	−1.20124	−	4.72148i			1.25614i	11.0031			2.55925	+	1.56532i	6.79700	+	3.92425i
197.3	−1.26757	−	2.19550i	−1.50271	−	0.861307i	−2.21348	+	3.83387i	2.53073	−	1.46112i	0.0138007	+	4.39098i		−	0.937410i	6.15272			1.51630	+	2.58860i	−6.41578	−	3.70415i
197.4	−1.26757	−	2.19550i	0.00544374	−	1.73204i	−2.21348	+	3.83387i	−2.53073	+	1.46112i	−3.80960	+	2.18354i			0.937410i	6.15272			−2.99994	−	0.0188576i	6.41578	+	3.70415i
197.5	−1.22254	−	2.11749i	−1.37504	−	1.05322i	−1.98919	+	3.44537i	−1.16544	+	0.672865i	−0.549148	+	4.19923i		−	2.71504i	4.83727			0.781465	+	2.89643i	2.84958	+	1.64520i
197.6	−1.22254	−	2.11749i	−0.224594	−	1.71743i	−1.98919	+	3.44537i	1.16544	−	0.672865i	−3.36207	+	2.57519i			2.71504i	4.83727			−2.89912	+	0.771447i	−2.84958	−	1.64520i
197.7	−1.21589	−	2.10598i	−1.50839	+	0.851323i	−1.95678	+	3.38923i	−2.15832	+	1.24611i	3.62691	+	2.14153i		−	4.93096i	4.65333			1.55050	−	2.56826i	5.24856	+	3.03025i
197.8	−1.21589	−	2.10598i	1.49146	−	0.880645i	−1.95678	+	3.38923i	2.15832	−	1.24611i	−3.66808	−	2.07023i			4.93096i	4.65333			1.44893	−	2.62690i	−5.24856	−	3.03025i
197.9	−1.19514	−	2.07004i	−0.898802	+	1.48059i	−1.85670	+	3.21589i	−2.17193	+	1.25397i	4.13907	+	0.0910427i			2.65442i	4.09548			−1.38431	−	2.66152i	5.19151	+	2.99732i
197.10	−1.19514	−	2.07004i	1.73163	−	0.0380889i	−1.85670	+	3.21589i	2.17193	−	1.25397i	−2.14838	−	3.53902i		−	2.65442i	4.09548			2.99710	−	0.131912i	−5.19151	−	2.99732i
197.11	−1.11716	−	1.93498i	0.686511	+	1.59019i	−1.49610	+	2.59133i	−0.636140	+	0.367275i	2.31004	−	3.10489i		−	1.30275i	2.21691			−2.05740	+	2.18337i	1.42134	+	0.820612i
197.12	−1.11716	−	1.93498i	1.03389	+	1.38963i	−1.49610	+	2.59133i	0.636140	−	0.367275i	1.53389	−	3.55300i			1.30275i	2.21691			−0.862148	+	2.87345i	−1.42134	−	0.820612i
197.13	−1.00748	−	1.74501i	−1.64530	+	0.541282i	−1.03004	+	1.78408i	1.60686	−	0.927720i	2.60215	+	2.32573i			1.64515i	0.121055			2.41403	−	1.78114i	−3.23776	−	1.86932i
197.14	−1.00748	−	1.74501i	1.29141	−	1.15423i	−1.03004	+	1.78408i	−1.60686	+	0.927720i	−3.31522	−	1.09066i		−	1.64515i	0.121055			0.335501	−	2.98118i	3.23776	+	1.86932i
197.15	−0.873606	−	1.51313i	−0.568916	+	1.63595i	−0.526375	+	0.911708i	3.14552	−	1.81607i	2.97241	−	0.568333i			1.70419i	−1.65505			−2.35267	−	1.86144i	−5.49590	−	3.17306i
197.16	−0.873606	−	1.51313i	1.70123	+	0.325280i	−0.526375	+	0.911708i	−3.14552	+	1.81607i	−0.994017	−	2.85835i		−	1.70419i	−1.65505			2.78839	+	1.10675i	5.49590	+	3.17306i
197.17	−0.849649	−	1.47164i	−1.53953	−	0.793637i	−0.443807	+	0.768696i	−3.73665	+	2.15735i	0.140113	+	2.93993i			3.70345i	−1.89028			1.74028	+	2.44365i	6.34968	+	3.66599i
197.18	−0.849649	−	1.47164i	0.0824532	−	1.73009i	−0.443807	+	0.768696i	3.73665	−	2.15735i	−2.61611	+	1.34863i		−	3.70345i	−1.89028			−2.98640	−	0.285303i	−6.34968	−	3.66599i
197.19	−0.796127	−	1.37893i	−1.71617	+	0.234005i	−0.267637	+	0.463560i	−0.555733	+	0.320852i	1.68897	+	2.18019i			0.0200664i	−2.33222			2.89048	−	0.803183i	0.884868	+	0.510879i
197.20	−0.796127	−	1.37893i	1.06074	−	1.36925i	−0.267637	+	0.463560i	0.555733	−	0.320852i	−2.73258	−	0.372595i		−	0.0200664i	−2.33222			−0.749665	−	2.90482i	−0.884868	−	0.510879i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.b	odd	2	1	inner
19.c	even	3	1	inner
33.d	even	2	1	inner
57.h	odd	6	1	inner
209.h	odd	6	1	inner
627.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	627.2.l.a	✓	152
3.b	odd	2	1	inner	627.2.l.a	✓	152
11.b	odd	2	1	inner	627.2.l.a	✓	152
19.c	even	3	1	inner	627.2.l.a	✓	152
33.d	even	2	1	inner	627.2.l.a	✓	152
57.h	odd	6	1	inner	627.2.l.a	✓	152
209.h	odd	6	1	inner	627.2.l.a	✓	152
627.l	even	6	1	inner	627.2.l.a	✓	152

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
627.2.l.a	✓	152	1.a	even	1	1	trivial
627.2.l.a	✓	152	3.b	odd	2	1	inner
627.2.l.a	✓	152	11.b	odd	2	1	inner
627.2.l.a	✓	152	19.c	even	3	1	inner
627.2.l.a	✓	152	33.d	even	2	1	inner
627.2.l.a	✓	152	57.h	odd	6	1	inner
627.2.l.a	✓	152	209.h	odd	6	1	inner
627.2.l.a	✓	152	627.l	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(627, [\chi])\).