Newform orbit 260.2.j.a

• Label: 260.2.j.a
• Level: $260$
• Weight: $2$
• Character orbit: 260.j
• Analytic conductor: $2.076$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.07611045255\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
31.1	−1.41372	−	0.0374414i			1.74175i	1.99720	+	0.105863i	−0.707107	+	0.707107i	0.0652137	−	2.46234i	−2.26642	+	2.26642i	−2.81951	−	0.224439i	−0.0336953			1.02612	−	0.973174i
31.2	−1.36090	−	0.384637i		−	1.17966i	1.70411	+	1.04691i	−0.707107	+	0.707107i	−0.453740	+	1.60540i	0.171101	−	0.171101i	−1.91645	−	2.08020i	1.60841			1.23428	−	0.690324i
31.3	−1.25736	+	0.647340i		−	0.759638i	1.16190	−	1.62788i	0.707107	−	0.707107i	0.491744	+	0.955138i	−2.17387	+	2.17387i	−0.407140	+	2.79897i	2.42295			−0.431349	+	1.34683i
31.4	−1.25602	−	0.649941i		−	2.18560i	1.15515	+	1.63267i	0.707107	−	0.707107i	−1.42051	+	2.74515i	1.49904	−	1.49904i	−0.389750	−	2.80145i	−1.77684			−1.34772	+	0.428560i
31.5	−1.22023	+	0.714871i			1.31885i	0.977920	−	1.74461i	−0.707107	+	0.707107i	−0.942808	−	1.60930i	3.16584	−	3.16584i	0.0538847	+	2.82791i	1.26063			0.357343	−	1.36832i
31.6	−1.20609	+	0.738473i			3.43622i	0.909314	−	1.78133i	0.707107	−	0.707107i	−2.53756	−	4.14440i	−1.29013	+	1.29013i	0.218751	+	2.81996i	−8.80762			−0.330656	+	1.37502i
31.7	−1.08931	−	0.901894i			0.947478i	0.373176	+	1.96488i	0.707107	−	0.707107i	0.854524	−	1.03209i	−2.28468	+	2.28468i	1.36561	−	2.47692i	2.10229			−1.40799	+	0.132521i
31.8	−0.853677	−	1.12749i		−	2.83163i	−0.542471	+	1.92503i	−0.707107	+	0.707107i	−3.19263	+	2.41729i	−2.55134	+	2.55134i	2.63354	−	1.03172i	−5.01810			1.40090	+	0.193616i
31.9	−0.738473	+	1.20609i		−	3.43622i	−0.909314	−	1.78133i	0.707107	−	0.707107i	4.14440	+	2.53756i	1.29013	−	1.29013i	2.81996	+	0.218751i	−8.80762			0.330656	+	1.37502i
31.10	−0.714871	+	1.22023i		−	1.31885i	−0.977920	−	1.74461i	−0.707107	+	0.707107i	1.60930	+	0.942808i	−3.16584	+	3.16584i	2.82791	+	0.0538847i	1.26063			−0.357343	−	1.36832i
31.11	−0.647340	+	1.25736i			0.759638i	−1.16190	−	1.62788i	0.707107	−	0.707107i	−0.955138	−	0.491744i	2.17387	−	2.17387i	2.79897	−	0.407140i	2.42295			0.431349	+	1.34683i
31.12	−0.551623	−	1.30220i			0.224099i	−1.39142	+	1.43664i	−0.707107	+	0.707107i	0.291821	−	0.123618i	−0.228458	+	0.228458i	2.63833	+	1.01942i	2.94978			1.31085	+	0.530735i
31.13	−0.329884	−	1.37520i			0.0805516i	−1.78235	+	0.907313i	0.707107	−	0.707107i	0.110775	−	0.0265727i	2.41026	−	2.41026i	1.83571	+	2.15179i	2.99351			−1.20568	−	0.739151i
31.14	0.0374414	+	1.41372i		−	1.74175i	−1.99720	+	0.105863i	−0.707107	+	0.707107i	2.46234	−	0.0652137i	2.26642	−	2.26642i	−0.224439	−	2.81951i	−0.0336953			−1.02612	−	0.973174i
31.15	0.0957733	−	1.41097i			2.67523i	−1.98165	−	0.270266i	−0.707107	+	0.707107i	3.77466	+	0.256215i	0.0140243	−	0.0140243i	−0.571126	+	2.77017i	−4.15684			0.929982	+	1.06543i
31.16	0.270865	−	1.38803i		−	2.58563i	−1.85326	−	0.751939i	0.707107	−	0.707107i	−3.58893	−	0.700357i	−1.49185	+	1.49185i	−1.54570	+	2.36871i	−3.68547			−0.789956	−	1.17302i
31.17	0.384637	+	1.36090i			1.17966i	−1.70411	+	1.04691i	−0.707107	+	0.707107i	−1.60540	+	0.453740i	−0.171101	+	0.171101i	−2.08020	−	1.91645i	1.60841			−1.23428	−	0.690324i
31.18	0.400070	−	1.35645i		−	2.57103i	−1.67989	−	1.08535i	−0.707107	+	0.707107i	−3.48746	−	1.02859i	3.59259	−	3.59259i	−2.14428	+	1.84446i	−3.61018			0.676260	+	1.24204i
31.19	0.649941	+	1.25602i			2.18560i	−1.15515	+	1.63267i	0.707107	−	0.707107i	−2.74515	+	1.42051i	−1.49904	+	1.49904i	−2.80145	−	0.389750i	−1.77684			1.34772	+	0.428560i
31.20	0.723264	−	1.21527i			1.80245i	−0.953778	−	1.75793i	0.707107	−	0.707107i	2.19047	+	1.30365i	1.20463	−	1.20463i	−2.82620	−	0.112344i	−0.248815			−0.347903	−	1.37075i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
13.d	odd	4	1	inner
52.f	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.j.a	✓	56
4.b	odd	2	1	inner	260.2.j.a	✓	56
13.d	odd	4	1	inner	260.2.j.a	✓	56
52.f	even	4	1	inner	260.2.j.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
260.2.j.a	✓	56	1.a	even	1	1	trivial
260.2.j.a	✓	56	4.b	odd	2	1	inner
260.2.j.a	✓	56	13.d	odd	4	1	inner
260.2.j.a	✓	56	52.f	even	4	1	inner

Hecke kernels

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