Newform orbit 819.2.db.a

• Label: 819.2.db.a
• Level: $819$
• Weight: $2$
• Character orbit: 819.db
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $192$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.db (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.53974792554\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(96\) 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.

\(\operatorname{Tr}(f)(q) = \) 192 * q + 96 * q^4 + 8 * q^9 + 18 * q^14 + 12 * q^15 - 96 * q^16 + 20 * q^18 + 22 * q^21 - 36 * q^23 - 96 * q^25 - 72 * q^29 - 52 * q^30 + 60 * q^32 - 12 * q^36 - 78 * q^42 + 48 * q^46 - 12 * q^49 + 96 * q^50 + 44 * q^51 - 60 * q^56 + 28 * q^57 - 24 * q^58 + 112 * q^60 - 68 * q^63 - 192 * q^64 + 56 * q^72 + 90 * q^77 - 20 * q^78 + 24 * q^79 - 32 * q^81 + 66 * q^84 + 60 * q^86 - 84 * q^92 - 116 * q^93 - 96 * q^95 + 28 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
209.1	−2.39694	−	1.38387i	−0.718814	+	1.57585i	2.83020	+	4.90206i	−1.26074	−	2.18367i	3.90373	−	2.78247i	0.0515663	−	2.64525i		−	10.1311i	−1.96661	−	2.26549i			6.97881i
209.2	−2.39694	−	1.38387i	0.718814	−	1.57585i	2.83020	+	4.90206i	1.26074	+	2.18367i	−3.90373	+	2.78247i	2.26507	−	1.36728i		−	10.1311i	−1.96661	−	2.26549i		−	6.97881i
209.3	−2.31896	−	1.33885i	−0.391650	−	1.68719i	2.58505	+	4.47744i	−1.03457	−	1.79192i	−1.35068	+	4.43689i	−1.25442	+	2.32947i		−	8.48860i	−2.69322	+	1.32158i			5.54054i
209.4	−2.31896	−	1.33885i	0.391650	+	1.68719i	2.58505	+	4.47744i	1.03457	+	1.79192i	1.35068	−	4.43689i	−1.39017	+	2.25109i		−	8.48860i	−2.69322	+	1.32158i		−	5.54054i
209.5	−2.30587	−	1.33130i	−1.66942	−	0.461561i	2.54470	+	4.40755i	−1.10336	−	1.91107i	3.23500	+	3.28679i	2.54699	+	0.716144i		−	8.22582i	2.57392	+	1.54108i			5.87558i
209.6	−2.30587	−	1.33130i	1.66942	+	0.461561i	2.54470	+	4.40755i	1.10336	+	1.91107i	−3.23500	−	3.28679i	−1.89369	−	1.84768i		−	8.22582i	2.57392	+	1.54108i		−	5.87558i
209.7	−2.13196	−	1.23089i	−1.56926	+	0.733092i	2.03018	+	3.51637i	1.18705	+	2.05603i	4.24796	+	0.368659i	−2.55819	−	0.675034i		−	5.07213i	1.92515	−	2.30082i		−	5.84449i
209.8	−2.13196	−	1.23089i	1.56926	−	0.733092i	2.03018	+	3.51637i	−1.18705	−	2.05603i	−4.24796	−	0.368659i	1.86369	+	1.87794i		−	5.07213i	1.92515	−	2.30082i			5.84449i
209.9	−2.13031	−	1.22994i	−1.27406	−	1.17336i	2.02549	+	3.50825i	2.06091	+	3.56960i	1.27098	+	4.06664i	−0.637652	+	2.56776i		−	5.04515i	0.246444	+	2.98986i		−	10.1392i
209.10	−2.13031	−	1.22994i	1.27406	+	1.17336i	2.02549	+	3.50825i	−2.06091	−	3.56960i	−1.27098	−	4.06664i	−1.90492	+	1.83610i		−	5.04515i	0.246444	+	2.98986i			10.1392i
209.11	−1.99802	−	1.15356i	−1.73164	+	0.0375373i	1.66138	+	2.87760i	0.966287	+	1.67366i	3.50316	+	1.92255i	2.15723	−	1.53178i		−	3.05176i	2.99718	−	0.130002i		−	4.45867i
209.12	−1.99802	−	1.15356i	1.73164	−	0.0375373i	1.66138	+	2.87760i	−0.966287	−	1.67366i	−3.50316	−	1.92255i	0.247942	−	2.63411i		−	3.05176i	2.99718	−	0.130002i			4.45867i
209.13	−1.86466	−	1.07656i	−1.44952	+	0.948095i	1.31797	+	2.28279i	−1.11192	−	1.92591i	3.72355	−	0.207373i	0.486211	+	2.60069i		−	1.36926i	1.20223	−	2.74857i			4.78822i
209.14	−1.86466	−	1.07656i	1.44952	−	0.948095i	1.31797	+	2.28279i	1.11192	+	1.92591i	−3.72355	+	0.207373i	−2.49537	+	0.879275i		−	1.36926i	1.20223	−	2.74857i		−	4.78822i
209.15	−1.80988	−	1.04493i	−0.741472	−	1.56532i	1.18377	+	2.05035i	−0.00831568	−	0.0144032i	−0.293679	+	3.60782i	1.62471	−	2.08814i		−	0.768117i	−1.90044	+	2.32128i			0.0347573i
209.16	−1.80988	−	1.04493i	0.741472	+	1.56532i	1.18377	+	2.05035i	0.00831568	+	0.0144032i	0.293679	−	3.60782i	0.996024	−	2.45111i		−	0.768117i	−1.90044	+	2.32128i		−	0.0347573i
209.17	−1.69552	−	0.978910i	−1.61632	−	0.622498i	0.916531	+	1.58748i	−1.77173	−	3.06872i	2.13114	+	2.63769i	−1.83923	−	1.90190i			0.326835i	2.22499	+	2.01231i			6.93745i
209.18	−1.69552	−	0.978910i	1.61632	+	0.622498i	0.916531	+	1.58748i	1.77173	+	3.06872i	−2.13114	−	2.63769i	2.56671	+	0.641874i			0.326835i	2.22499	+	2.01231i		−	6.93745i
209.19	−1.51519	−	0.874794i	−0.721994	−	1.57440i	0.530529	+	0.918903i	0.00733371	+	0.0127024i	−0.283317	+	3.01710i	1.80568	+	1.93378i			1.64276i	−1.95745	+	2.27341i		−	0.0256619i
209.20	−1.51519	−	0.874794i	0.721994	+	1.57440i	0.530529	+	0.918903i	−0.00733371	−	0.0127024i	0.283317	−	3.01710i	−2.57754	−	0.596879i			1.64276i	−1.95745	+	2.27341i			0.0256619i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
9.d	odd	6	1	inner
63.o	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	819.2.db.a	✓	192
7.b	odd	2	1	inner	819.2.db.a	✓	192
9.d	odd	6	1	inner	819.2.db.a	✓	192
63.o	even	6	1	inner	819.2.db.a	✓	192

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
819.2.db.a	✓	192	1.a	even	1	1	trivial
819.2.db.a	✓	192	7.b	odd	2	1	inner
819.2.db.a	✓	192	9.d	odd	6	1	inner
819.2.db.a	✓	192	63.o	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(819, [\chi])\).