Newform orbit 430.2.j.a

• Label: 430.2.j.a
• Level: $430$
• Weight: $2$
• Character orbit: 430.j
• Analytic conductor: $3.434$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.43356728692\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
49.1		−	1.00000i	−2.75803	−	1.59235i	−1.00000			1.06925	+	1.96385i	−1.59235	+	2.75803i	3.76835	−	2.17566i			1.00000i	3.57116	+	6.18543i	1.96385	−	1.06925i
49.2		−	1.00000i	−2.19536	−	1.26749i	−1.00000			0.795101	−	2.08993i	−1.26749	+	2.19536i	−2.46471	+	1.42300i			1.00000i	1.71308	+	2.96715i	−2.08993	−	0.795101i
49.3		−	1.00000i	−1.92330	−	1.11042i	−1.00000			−2.17265	+	0.528758i	−1.11042	+	1.92330i	−1.64658	+	0.950651i			1.00000i	0.966065	+	1.67327i	0.528758	+	2.17265i
49.4		−	1.00000i	−0.409934	−	0.236675i	−1.00000			−1.79811	+	1.32921i	−0.236675	+	0.409934i	2.61255	−	1.50836i			1.00000i	−1.38797	−	2.40403i	1.32921	+	1.79811i
49.5		−	1.00000i	−0.377570	−	0.217990i	−1.00000			2.13668	−	0.659257i	−0.217990	+	0.377570i	0.236341	−	0.136452i			1.00000i	−1.40496	−	2.43346i	−0.659257	−	2.13668i
49.6		−	1.00000i	0.0417606	+	0.0241105i	−1.00000			0.704124	+	2.12231i	0.0241105	−	0.0417606i	−3.51224	+	2.02779i			1.00000i	−1.49884	−	2.59606i	2.12231	−	0.704124i
49.7		−	1.00000i	1.09428	+	0.631780i	−1.00000			0.410590	−	2.19805i	0.631780	−	1.09428i	2.36788	−	1.36710i			1.00000i	−0.701708	−	1.21539i	−2.19805	−	0.410590i
49.8		−	1.00000i	1.13990	+	0.658124i	−1.00000			−1.72456	−	1.42334i	0.658124	−	1.13990i	−3.46526	+	2.00067i			1.00000i	−0.633745	−	1.09768i	−1.42334	+	1.72456i
49.9		−	1.00000i	1.66171	+	0.959389i	−1.00000			−2.16132	−	0.573330i	0.959389	−	1.66171i	0.863309	−	0.498432i			1.00000i	0.340854	+	0.590377i	−0.573330	+	2.16132i
49.10		−	1.00000i	2.23224	+	1.28878i	−1.00000			−0.429629	+	2.19441i	1.28878	−	2.23224i	2.28550	−	1.31953i			1.00000i	1.82193	+	3.15567i	2.19441	+	0.429629i
49.11		−	1.00000i	2.36034	+	1.36274i	−1.00000			2.17053	+	0.537418i	1.36274	−	2.36034i	−2.77719	+	1.60341i			1.00000i	2.21413	+	3.83499i	0.537418	−	2.17053i
49.12			1.00000i	−2.36034	−	1.36274i	−1.00000			−1.55068	−	1.61102i	1.36274	−	2.36034i	2.77719	−	1.60341i		−	1.00000i	2.21413	+	3.83499i	1.61102	−	1.55068i
49.13			1.00000i	−2.23224	−	1.28878i	−1.00000			−1.68560	+	1.46927i	1.28878	−	2.23224i	−2.28550	+	1.31953i		−	1.00000i	1.82193	+	3.15567i	−1.46927	−	1.68560i
49.14			1.00000i	−1.66171	−	0.959389i	−1.00000			1.57718	+	1.58509i	0.959389	−	1.66171i	−0.863309	+	0.498432i		−	1.00000i	0.340854	+	0.590377i	−1.58509	+	1.57718i
49.15			1.00000i	−1.13990	−	0.658124i	−1.00000			2.09493	+	0.781842i	0.658124	−	1.13990i	3.46526	−	2.00067i		−	1.00000i	−0.633745	−	1.09768i	−0.781842	+	2.09493i
49.16			1.00000i	−1.09428	−	0.631780i	−1.00000			1.69827	−	1.45461i	0.631780	−	1.09428i	−2.36788	+	1.36710i		−	1.00000i	−0.701708	−	1.21539i	1.45461	+	1.69827i
49.17			1.00000i	−0.0417606	−	0.0241105i	−1.00000			−2.19004	+	0.451367i	0.0241105	−	0.0417606i	3.51224	−	2.02779i		−	1.00000i	−1.49884	−	2.59606i	−0.451367	−	2.19004i
49.18			1.00000i	0.377570	+	0.217990i	−1.00000			−0.497404	−	2.18004i	−0.217990	+	0.377570i	−0.236341	+	0.136452i		−	1.00000i	−1.40496	−	2.43346i	2.18004	−	0.497404i
49.19			1.00000i	0.409934	+	0.236675i	−1.00000			−0.252079	+	2.22181i	−0.236675	+	0.409934i	−2.61255	+	1.50836i		−	1.00000i	−1.38797	−	2.40403i	−2.22181	−	0.252079i
49.20			1.00000i	1.92330	+	1.11042i	−1.00000			0.628408	+	2.14595i	−1.11042	+	1.92330i	1.64658	−	0.950651i		−	1.00000i	0.966065	+	1.67327i	−2.14595	+	0.628408i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
43.c	even	3	1	inner
215.i	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	430.2.j.a	✓	44
5.b	even	2	1	inner	430.2.j.a	✓	44
43.c	even	3	1	inner	430.2.j.a	✓	44
215.i	even	6	1	inner	430.2.j.a	✓	44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
430.2.j.a	✓	44	1.a	even	1	1	trivial
430.2.j.a	✓	44	5.b	even	2	1	inner
430.2.j.a	✓	44	43.c	even	3	1	inner
430.2.j.a	✓	44	215.i	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(430, [\chi])\).