Newform orbit 187.3.i.a

• Label: 187.3.i.a
• Level: $187$
• Weight: $3$
• Character orbit: 187.i
• Analytic conductor: $5.095$
• Analytic rank: $0$
• Dimension: $136$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	187.i (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.09538094354\)
Analytic rank:	\(0\)
Dimension:	\(136\)
Relative dimension:	\(34\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 136 q - 8 q^{3} - 56 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−2.75457	+	2.75457i	1.77698	+	4.29000i		−	11.1753i	6.58362	−	2.72703i	−16.7119	−	6.92231i	2.96702	−	7.16302i	19.7649	+	19.7649i	−8.88253	+	8.88253i	−10.6233	+	25.6468i
32.2	−2.58893	+	2.58893i	0.800848	+	1.93342i		−	9.40514i	−5.26536	+	2.18098i	−7.07883	−	2.93215i	−5.29643	+	12.7867i	13.9935	+	13.9935i	3.26721	−	3.26721i	7.98523	−	19.2781i
32.3	−2.56223	+	2.56223i	−1.00069	−	2.41587i		−	9.13002i	−3.43971	+	1.42478i	8.75401	+	3.62603i	1.46134	−	3.52799i	13.1443	+	13.1443i	1.52889	−	1.52889i	5.16273	−	12.4639i
32.4	−2.33830	+	2.33830i	−1.57303	−	3.79763i		−	6.93527i	5.52416	−	2.28818i	12.5582	+	5.20177i	1.07637	−	2.59858i	6.86353	+	6.86353i	−5.58358	+	5.58358i	−7.56668	+	18.2676i
32.5	−2.19570	+	2.19570i	0.405725	+	0.979506i		−	5.64217i	2.05816	−	0.852516i	−3.04155	−	1.25985i	0.178235	−	0.430296i	3.60571	+	3.60571i	5.56914	−	5.56914i	−2.64722	+	6.39095i
32.6	−1.98269	+	1.98269i	1.79483	+	4.33311i		−	3.86211i	−7.36046	+	3.04880i	−12.1498	−	5.03261i	3.25999	−	7.87031i	−0.273394	−	0.273394i	−9.19043	+	9.19043i	8.54867	−	20.6383i
32.7	−1.90829	+	1.90829i	−2.01079	−	4.85448i		−	3.28318i	−5.80231	+	2.40340i	13.1010	+	5.42660i	−2.56478	+	6.19193i	−1.36791	−	1.36791i	−13.1587	+	13.1587i	6.48613	−	15.6589i
32.8	−1.59422	+	1.59422i	1.42946	+	3.45103i		−	1.08308i	−0.503888	+	0.208717i	−7.78057	−	3.22282i	−1.34429	+	3.24540i	−4.65022	−	4.65022i	−3.50226	+	3.50226i	0.470568	−	1.13605i
32.9	−1.55201	+	1.55201i	−0.502892	−	1.21409i		−	0.817477i	3.08661	−	1.27852i	2.66477	+	1.10379i	−2.97599	+	7.18468i	−4.93931	−	4.93931i	5.14285	−	5.14285i	−2.80618	+	6.77473i
32.10	−1.32570	+	1.32570i	−0.512569	−	1.23745i			0.485044i	−8.37529	+	3.46916i	2.32000	+	0.960975i	2.41387	−	5.82760i	−5.94582	−	5.94582i	5.09540	−	5.09540i	6.50405	−	15.7022i
32.11	−1.29803	+	1.29803i	0.186881	+	0.451171i			0.630257i	2.16414	−	0.896415i	−0.828209	−	0.343055i	4.54586	−	10.9747i	−6.01019	−	6.01019i	6.19533	−	6.19533i	−1.64554	+	3.97268i
32.12	−1.20269	+	1.20269i	2.16633	+	5.22997i			1.10709i	4.48917	−	1.85948i	−8.89542	−	3.68460i	−3.23345	+	7.80624i	−6.14223	−	6.14223i	−16.2957	+	16.2957i	−3.16270	+	7.63543i
32.13	−0.918528	+	0.918528i	−1.51387	−	3.65481i			2.31261i	7.38627	−	3.05949i	4.74758	+	1.96651i	−1.13519	+	2.74060i	−5.79831	−	5.79831i	−4.70185	+	4.70185i	−3.97426	+	9.59472i
32.14	−0.632661	+	0.632661i	−0.597925	−	1.44352i			3.19948i	−2.40471	+	0.996065i	1.29154	+	0.534974i	−2.46135	+	5.94223i	−4.55483	−	4.55483i	4.63773	−	4.63773i	0.891196	−	2.15154i
32.15	−0.318963	+	0.318963i	0.763482	+	1.84321i			3.79653i	7.19173	−	2.97891i	−0.831438	−	0.344393i	3.30210	−	7.97197i	−2.48680	−	2.48680i	3.54945	−	3.54945i	−1.34373	+	3.24406i
32.16	−0.309209	+	0.309209i	−1.84294	−	4.44925i			3.80878i	−1.37895	+	0.571180i	1.94560	+	0.805896i	3.22987	−	7.79760i	−2.41455	−	2.41455i	−10.0354	+	10.0354i	0.249770	−	0.602999i
32.17	−0.0549292	+	0.0549292i	1.35149	+	3.26279i			3.99397i	−3.95318	+	1.63746i	−0.253459	−	0.104986i	−0.624098	+	1.50671i	−0.439102	−	0.439102i	−2.45531	+	2.45531i	0.127201	−	0.307090i
32.18	0.0549292	−	0.0549292i	1.35149	+	3.26279i			3.99397i	−3.95318	+	1.63746i	0.253459	+	0.104986i	0.624098	−	1.50671i	0.439102	+	0.439102i	−2.45531	+	2.45531i	−0.127201	+	0.307090i
32.19	0.309209	−	0.309209i	−1.84294	−	4.44925i			3.80878i	−1.37895	+	0.571180i	−1.94560	−	0.805896i	−3.22987	+	7.79760i	2.41455	+	2.41455i	−10.0354	+	10.0354i	−0.249770	+	0.602999i
32.20	0.318963	−	0.318963i	0.763482	+	1.84321i			3.79653i	7.19173	−	2.97891i	0.831438	+	0.344393i	−3.30210	+	7.97197i	2.48680	+	2.48680i	3.54945	−	3.54945i	1.34373	−	3.24406i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
17.d	even	8	1	inner
187.i	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	187.3.i.a	✓	136
11.b	odd	2	1	inner	187.3.i.a	✓	136
17.d	even	8	1	inner	187.3.i.a	✓	136
187.i	odd	8	1	inner	187.3.i.a	✓	136

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
187.3.i.a	✓	136	1.a	even	1	1	trivial
187.3.i.a	✓	136	11.b	odd	2	1	inner
187.3.i.a	✓	136	17.d	even	8	1	inner
187.3.i.a	✓	136	187.i	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(187, [\chi])\).