Newform orbit 115.3.i.a

• Label: 115.3.i.a
• Level: $115$
• Weight: $3$
• Character orbit: 115.i
• Analytic conductor: $3.134$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.13352304014\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(22\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−1.06616	−	3.63102i	−3.98118	+	3.44971i	−8.68261	+	5.57997i	4.33958	−	2.48356i	16.7706	+	10.7778i	−0.608324	+	1.33204i	18.0781	+	15.6648i	2.66845	−	18.5594i	−13.6446	−	13.1092i
14.2	−1.01059	−	3.44174i	−0.190798	+	0.165327i	−7.45930	+	4.79380i	−4.45644	+	2.26720i	0.761832	+	0.489600i	0.896990	−	1.96413i	13.1937	+	11.4324i	−1.27176	+	8.84530i	12.3067	+	13.0467i
14.3	−0.909272	−	3.09670i	2.61799	−	2.26850i	−5.39774	+	3.46891i	0.569021	−	4.96752i	−9.40531	−	6.04443i	−1.76617	+	3.86736i	5.89367	+	5.10690i	0.426936	−	2.96941i	−15.9003	+	2.75474i
14.4	−0.761060	−	2.59193i	4.31740	−	3.74105i	−2.77389	+	1.78267i	−0.640865	+	4.95876i	−12.9823	−	8.34325i	1.74741	−	3.82629i	−1.43453	−	1.24303i	3.36366	−	23.3948i	13.3405	−	2.11284i
14.5	−0.723107	−	2.46268i	−0.136015	+	0.117858i	−2.17688	+	1.39899i	4.86226	+	1.16552i	0.388600	+	0.249738i	4.52870	−	9.91648i	−2.73958	−	2.37386i	−1.27622	+	8.87633i	−0.645632	−	12.8170i
14.6	−0.636390	−	2.16735i	−2.13320	+	1.84843i	−0.927382	+	0.595992i	−2.88883	−	4.08101i	5.36373	+	3.44706i	−1.73429	+	3.79756i	−4.94659	−	4.28624i	−0.146981	+	1.02227i	−7.00655	+	8.85821i
14.7	−0.618956	−	2.10797i	−1.36297	+	1.18102i	−0.695419	+	0.446919i	1.65130	+	4.71945i	3.33318	+	2.14211i	−4.87531	+	10.6754i	−5.26889	−	4.56552i	−0.817952	+	5.68898i	8.92638	−	6.40203i
14.8	−0.435846	−	1.48436i	−4.32985	+	3.75184i	1.35166	−	0.868661i	−3.10020	+	3.92285i	7.45621	+	4.79182i	4.16584	−	9.12191i	−6.55516	−	5.68008i	3.39049	−	23.5814i	7.17412	+	2.89204i
14.9	−0.254893	−	0.868087i	1.66868	−	1.44592i	2.67641	−	1.72002i	−4.78864	−	1.43838i	−1.68052	−	1.08001i	2.63365	−	5.76689i	−4.91034	−	4.25483i	−0.587022	+	4.08283i	−0.0280477	+	4.52359i
14.10	−0.245567	−	0.836325i	2.37235	−	2.05565i	2.72588	−	1.75182i	4.33861	−	2.48524i	−2.30176	−	1.47925i	−2.30176	+	5.04015i	−4.76942	−	4.13272i	0.121499	−	0.845043i	−3.14389	−	3.01820i
14.11	−0.0253139	−	0.0862113i	−2.10252	+	1.82185i	3.35822	−	2.15820i	0.240436	−	4.99422i	0.210287	+	0.135143i	0.329456	−	0.721408i	−0.542690	−	0.470243i	−0.179355	+	1.24744i	−0.436644	+	0.105695i
14.12	0.0253139	+	0.0862113i	2.10252	−	1.82185i	3.35822	−	2.15820i	1.63773	+	4.72418i	0.210287	+	0.135143i	−0.329456	+	0.721408i	0.542690	+	0.470243i	−0.179355	+	1.24744i	−0.365820	+	0.260778i
14.13	0.245567	+	0.836325i	−2.37235	+	2.05565i	2.72588	−	1.75182i	4.86304	+	1.16224i	−2.30176	−	1.47925i	2.30176	−	5.04015i	4.76942	+	4.13272i	0.121499	−	0.845043i	0.222190	+	4.35249i
14.14	0.254893	+	0.868087i	−1.66868	+	1.44592i	2.67641	−	1.72002i	−4.18943	+	2.72923i	−1.68052	−	1.08001i	−2.63365	+	5.76689i	4.91034	+	4.25483i	−0.587022	+	4.08283i	−3.43707	−	2.94112i
14.15	0.435846	+	1.48436i	4.32985	−	3.75184i	1.35166	−	0.868661i	−4.07982	−	2.89052i	7.45621	+	4.79182i	−4.16584	+	9.12191i	6.55516	+	5.68008i	3.39049	−	23.5814i	2.51239	−	7.31572i
14.16	0.618956	+	2.10797i	1.36297	−	1.18102i	−0.695419	+	0.446919i	0.254791	−	4.99350i	3.33318	+	2.14211i	4.87531	−	10.6754i	5.26889	+	4.56552i	−0.817952	+	5.68898i	10.6839	−	2.55367i
14.17	0.636390	+	2.16735i	2.13320	−	1.84843i	−0.927382	+	0.595992i	−1.62206	+	4.72958i	5.36373	+	3.44706i	1.73429	−	3.79756i	4.94659	+	4.28624i	−0.146981	+	1.02227i	−11.2829	−	0.505697i
14.18	0.723107	+	2.46268i	0.136015	−	0.117858i	−2.17688	+	1.39899i	4.33694	−	2.48817i	0.388600	+	0.249738i	−4.52870	+	9.91648i	2.73958	+	2.37386i	−1.27622	+	8.87633i	9.26362	+	8.88126i
14.19	0.761060	+	2.59193i	−4.31740	+	3.74105i	−2.77389	+	1.78267i	−2.01195	−	4.57734i	−12.9823	−	8.34325i	−1.74741	+	3.82629i	1.43453	+	1.24303i	3.36366	−	23.3948i	10.3330	−	8.69847i
14.20	0.909272	+	3.09670i	−2.61799	+	2.26850i	−5.39774	+	3.46891i	1.94548	+	4.60598i	−9.40531	−	6.04443i	1.76617	−	3.86736i	−5.89367	−	5.10690i	0.426936	−	2.96941i	−12.4944	+	10.2127i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
23.d	odd	22	1	inner
115.i	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	115.3.i.a	✓	220
5.b	even	2	1	inner	115.3.i.a	✓	220
23.d	odd	22	1	inner	115.3.i.a	✓	220
115.i	odd	22	1	inner	115.3.i.a	✓	220

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
115.3.i.a	✓	220	1.a	even	1	1	trivial
115.3.i.a	✓	220	5.b	even	2	1	inner
115.3.i.a	✓	220	23.d	odd	22	1	inner
115.3.i.a	✓	220	115.i	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(115, [\chi])\).