Newform orbit 260.2.o.a

• Label: 260.2.o.a
• Level: $260$
• Weight: $2$
• Character orbit: 260.o
• Analytic conductor: $2.076$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.07611045255\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
27.1	−1.41404	+	0.0221303i	0.798638	+	0.798638i	1.99902	−	0.0625863i	−1.57330	−	1.58893i	−1.14698	−	1.11163i	1.30625	−	1.30625i	−2.82531	+	0.132739i		−	1.72435i	2.25988	+	2.21200i
27.2	−1.41202	−	0.0788259i	−1.63309	−	1.63309i	1.98757	+	0.222607i	−0.963620	+	2.01778i	2.17721	+	2.43467i	3.04756	−	3.04756i	−2.78894	−	0.470996i			2.33394i	1.51970	−	2.77318i
27.3	−1.39950	+	0.203483i	0.0775283	+	0.0775283i	1.91719	−	0.569548i	0.871245	+	2.05935i	−0.124276	−	0.0927250i	−2.89635	+	2.89635i	−2.56721	+	1.18720i		−	2.98798i	−1.63835	−	2.70478i
27.4	−1.34983	−	0.421862i	−1.90910	−	1.90910i	1.64407	+	1.13888i	−0.987103	−	2.00640i	1.77158	+	3.38234i	−3.15102	+	3.15102i	−1.73875	−	2.23086i			4.28935i	0.485997	+	3.12471i
27.5	−1.32767	−	0.487116i	0.396814	+	0.396814i	1.52544	+	1.29346i	2.02359	−	0.951360i	−0.333545	−	0.720134i	0.477103	−	0.477103i	−1.39521	−	2.46036i		−	2.68508i	−3.15009	+	0.277373i
27.6	−1.26622	+	0.629837i	2.21225	+	2.21225i	1.20661	−	1.59502i	1.36305	−	1.77259i	−4.19454	−	1.40783i	−2.47925	+	2.47925i	−0.523229	+	2.77961i			6.78807i	−0.609477	+	3.10299i
27.7	−1.23527	+	0.688553i	−1.59413	−	1.59413i	1.05179	−	1.70110i	1.94514	−	1.10291i	3.06682	+	0.871538i	0.0942377	−	0.0942377i	−0.127946	+	2.82553i			2.08249i	−1.64337	+	2.70173i
27.8	−1.18329	−	0.774482i	2.05925	+	2.05925i	0.800354	+	1.83288i	1.34695	+	1.78486i	−0.841839	−	4.03155i	0.845670	−	0.845670i	0.472478	−	2.78869i			5.48103i	−0.211491	−	3.15520i
27.9	−1.08734	+	0.904262i	1.78782	+	1.78782i	0.364619	−	1.96648i	−1.34049	+	1.78972i	−3.56063	−	0.327311i	2.34459	−	2.34459i	1.38175	+	2.46795i			3.39260i	−0.160802	−	3.15819i
27.10	−0.942648	+	1.05424i	0.158208	+	0.158208i	−0.222831	−	1.98755i	−2.23604	+	0.0111104i	−0.315922	+	0.0176543i	−2.20671	+	2.20671i	2.30540	+	1.63864i		−	2.94994i	2.09608	−	2.36779i
27.11	−0.774482	−	1.18329i	−2.05925	−	2.05925i	−0.800354	+	1.83288i	1.34695	+	1.78486i	−0.841839	+	4.03155i	−0.845670	+	0.845670i	2.78869	−	0.472478i			5.48103i	1.06882	−	2.97618i
27.12	−0.769019	+	1.18685i	−0.808783	−	0.808783i	−0.817219	−	1.82542i	0.885949	+	2.05307i	1.58187	−	0.337933i	0.771151	−	0.771151i	2.79495	+	0.433867i		−	1.69174i	−3.11799	−	0.527363i
27.13	−0.516756	+	1.31642i	−2.23963	−	2.23963i	−1.46593	−	1.36054i	−2.20168	−	0.390628i	4.10564	−	1.79095i	0.918543	−	0.918543i	2.54856	−	1.22671i			7.03189i	1.65196	−	2.69648i
27.14	−0.505980	+	1.32060i	0.658144	+	0.658144i	−1.48797	−	1.33639i	0.820865	−	2.07995i	−1.20215	+	0.536137i	1.89124	−	1.89124i	2.51772	−	1.28882i		−	2.13369i	2.33144	+	2.13645i
27.15	−0.487116	−	1.32767i	−0.396814	−	0.396814i	−1.52544	+	1.29346i	2.02359	−	0.951360i	−0.333545	+	0.720134i	−0.477103	+	0.477103i	2.46036	+	1.39521i		−	2.68508i	−2.24882	−	2.22324i
27.16	−0.421862	−	1.34983i	1.90910	+	1.90910i	−1.64407	+	1.13888i	−0.987103	−	2.00640i	1.77158	−	3.38234i	3.15102	−	3.15102i	2.23086	+	1.73875i			4.28935i	−2.29187	+	2.17884i
27.17	−0.0788259	−	1.41202i	1.63309	+	1.63309i	−1.98757	+	0.222607i	−0.963620	+	2.01778i	2.17721	−	2.43467i	−3.04756	+	3.04756i	0.470996	+	2.78894i			2.33394i	2.92509	+	1.20159i
27.18	−0.0447185	+	1.41351i	1.60820	+	1.60820i	−1.99600	−	0.126420i	1.86263	+	1.23718i	−2.34511	+	2.20128i	−0.275770	+	0.275770i	0.267954	−	2.81571i			2.17259i	−1.83206	+	2.57751i
27.19	0.0221303	−	1.41404i	−0.798638	−	0.798638i	−1.99902	−	0.0625863i	−1.57330	−	1.58893i	−1.14698	+	1.11163i	−1.30625	+	1.30625i	−0.132739	+	2.82531i		−	1.72435i	−2.28164	+	2.18955i
27.20	0.203483	−	1.39950i	−0.0775283	−	0.0775283i	−1.91719	−	0.569548i	0.871245	+	2.05935i	−0.124276	+	0.0927250i	2.89635	−	2.89635i	−1.18720	+	2.56721i		−	2.98798i	3.05934	−	0.800263i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
20.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	260.2.o.a	✓	72
4.b	odd	2	1	inner	260.2.o.a	✓	72
5.c	odd	4	1	inner	260.2.o.a	✓	72
20.e	even	4	1	inner	260.2.o.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
260.2.o.a	✓	72	1.a	even	1	1	trivial
260.2.o.a	✓	72	4.b	odd	2	1	inner
260.2.o.a	✓	72	5.c	odd	4	1	inner
260.2.o.a	✓	72	20.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(260, [\chi])\).