Newform orbit 231.2.u.a

• Label: 231.2.u.a
• Level: $231$
• Weight: $2$
• Character orbit: 231.u
• Analytic conductor: $1.845$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.84454428669\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
20.1	−2.38523	−	0.775008i	−1.70548	−	0.302226i	3.47065	+	2.52157i	−0.223123	−	0.686701i	3.83373	+	2.04264i	−2.41111	+	1.08928i	−3.37575	−	4.64631i	2.81732	+	1.03088i			1.81086i
20.2	−2.38523	−	0.775008i	1.70548	+	0.302226i	3.47065	+	2.52157i	0.223123	+	0.686701i	−3.83373	−	2.04264i	0.290890	−	2.62971i	−3.37575	−	4.64631i	2.81732	+	1.03088i		−	1.81086i
20.3	−2.06683	−	0.671554i	−0.0708238	−	1.73060i	2.20277	+	1.60041i	−1.17677	−	3.62171i	−1.01581	+	3.62443i	1.06501	−	2.42193i	−0.923256	−	1.27075i	−2.98997	+	0.245136i			8.27573i
20.4	−2.06683	−	0.671554i	0.0708238	+	1.73060i	2.20277	+	1.60041i	1.17677	+	3.62171i	1.01581	−	3.62443i	−1.97429	+	1.76130i	−0.923256	−	1.27075i	−2.98997	+	0.245136i		−	8.27573i
20.5	−1.64177	−	0.533443i	−1.71497	−	0.242653i	0.792810	+	0.576010i	0.0901224	+	0.277368i	2.68614	+	1.31322i	2.64157	+	0.148745i	1.03500	+	1.42455i	2.88224	+	0.832286i		−	0.503450i
20.6	−1.64177	−	0.533443i	1.71497	+	0.242653i	0.792810	+	0.576010i	−0.0901224	−	0.277368i	−2.68614	−	1.31322i	0.957754	+	2.46631i	1.03500	+	1.42455i	2.88224	+	0.832286i			0.503450i
20.7	−1.48714	−	0.483201i	−0.691398	−	1.58807i	0.360067	+	0.261604i	0.748085	+	2.30237i	0.260847	+	2.69577i	−2.45500	−	0.986383i	1.42914	+	1.96705i	−2.04394	+	2.19598i		−	3.78542i
20.8	−1.48714	−	0.483201i	0.691398	+	1.58807i	0.360067	+	0.261604i	−0.748085	−	2.30237i	−0.260847	−	2.69577i	−1.69674	−	2.03004i	1.42914	+	1.96705i	−2.04394	+	2.19598i			3.78542i
20.9	−1.17237	−	0.380926i	−1.03573	+	1.38826i	−0.388687	−	0.282397i	−0.966595	−	2.97487i	1.74309	−	1.23301i	0.481870	+	2.60150i	1.79724	+	2.47369i	−0.854517	−	2.87573i			3.85585i
20.10	−1.17237	−	0.380926i	1.03573	−	1.38826i	−0.388687	−	0.282397i	0.966595	+	2.97487i	−1.74309	+	1.23301i	2.62308	−	0.345622i	1.79724	+	2.47369i	−0.854517	−	2.87573i		−	3.85585i
20.11	−0.606621	−	0.197103i	−1.17667	+	1.27100i	−1.28889	−	0.936436i	0.284064	+	0.874260i	0.964313	−	0.539091i	−0.678241	−	2.55734i	1.34712	+	1.85415i	−0.230890	−	2.99110i		−	0.586335i
20.12	−0.606621	−	0.197103i	1.17667	−	1.27100i	−1.28889	−	0.936436i	−0.284064	−	0.874260i	−0.964313	+	0.539091i	−2.64176	+	0.145216i	1.34712	+	1.85415i	−0.230890	−	2.99110i			0.586335i
20.13	−0.126891	−	0.0412293i	−0.347648	−	1.69680i	−1.60363	−	1.16511i	−0.887927	−	2.73276i	−0.0258447	+	0.229642i	0.380318	+	2.61827i	0.312296	+	0.429838i	−2.75828	+	1.17978i			0.383371i
20.14	−0.126891	−	0.0412293i	0.347648	+	1.69680i	−1.60363	−	1.16511i	0.887927	+	2.73276i	0.0258447	−	0.229642i	2.60765	−	0.447387i	0.312296	+	0.429838i	−2.75828	+	1.17978i		−	0.383371i
20.15	0.126891	+	0.0412293i	−1.50633	−	0.854974i	−1.60363	−	1.16511i	0.887927	+	2.73276i	−0.155889	−	0.170593i	0.380318	+	2.61827i	−0.312296	−	0.429838i	1.53804	+	2.57574i			0.383371i
20.16	0.126891	+	0.0412293i	1.50633	+	0.854974i	−1.60363	−	1.16511i	−0.887927	−	2.73276i	0.155889	+	0.170593i	2.60765	−	0.447387i	−0.312296	−	0.429838i	1.53804	+	2.57574i		−	0.383371i
20.17	0.606621	+	0.197103i	−1.57241	+	0.726320i	−1.28889	−	0.936436i	0.284064	+	0.874260i	−1.09702	+	0.130675i	−2.64176	+	0.145216i	−1.34712	−	1.85415i	1.94492	−	2.28414i			0.586335i
20.18	0.606621	+	0.197103i	1.57241	−	0.726320i	−1.28889	−	0.936436i	−0.284064	−	0.874260i	1.09702	−	0.130675i	−0.678241	−	2.55734i	−1.34712	−	1.85415i	1.94492	−	2.28414i		−	0.586335i
20.19	1.17237	+	0.380926i	−1.64037	+	0.556045i	−0.388687	−	0.282397i	−0.966595	−	2.97487i	−2.13493	+	0.0270304i	2.62308	−	0.345622i	−1.79724	−	2.47369i	2.38163	−	1.82424i		−	3.85585i
20.20	1.17237	+	0.380926i	1.64037	−	0.556045i	−0.388687	−	0.282397i	0.966595	+	2.97487i	2.13493	−	0.0270304i	0.481870	+	2.60150i	−1.79724	−	2.47369i	2.38163	−	1.82424i			3.85585i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
11.c	even	5	1	inner
21.c	even	2	1	inner
33.h	odd	10	1	inner
77.j	odd	10	1	inner
231.u	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	231.2.u.a	✓	112
3.b	odd	2	1	inner	231.2.u.a	✓	112
7.b	odd	2	1	inner	231.2.u.a	✓	112
11.c	even	5	1	inner	231.2.u.a	✓	112
21.c	even	2	1	inner	231.2.u.a	✓	112
33.h	odd	10	1	inner	231.2.u.a	✓	112
77.j	odd	10	1	inner	231.2.u.a	✓	112
231.u	even	10	1	inner	231.2.u.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
231.2.u.a	✓	112	1.a	even	1	1	trivial
231.2.u.a	✓	112	3.b	odd	2	1	inner
231.2.u.a	✓	112	7.b	odd	2	1	inner
231.2.u.a	✓	112	11.c	even	5	1	inner
231.2.u.a	✓	112	21.c	even	2	1	inner
231.2.u.a	✓	112	33.h	odd	10	1	inner
231.2.u.a	✓	112	77.j	odd	10	1	inner
231.2.u.a	✓	112	231.u	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(231, [\chi])\).