Newform orbit 210.3.v.a

• Label: 210.3.v.a
• Level: $210$
• Weight: $3$
• Character orbit: 210.v
• Analytic conductor: $5.722$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.72208555157\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 16 q^{2} - 8 q^{7} - 64 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−1.36603	+	0.366025i	−1.67303	−	0.448288i	1.73205	−	1.00000i	−4.60436	−	1.94932i	2.44949			−4.28537	−	5.53495i	−2.00000	+	2.00000i	2.59808	+	1.50000i	7.00318	+	0.977504i
37.2	−1.36603	+	0.366025i	−1.67303	−	0.448288i	1.73205	−	1.00000i	−1.25847	−	4.83903i	2.44949			5.72194	+	4.03230i	−2.00000	+	2.00000i	2.59808	+	1.50000i	3.49032	+	6.14961i
37.3	−1.36603	+	0.366025i	−1.67303	−	0.448288i	1.73205	−	1.00000i	−0.438103	+	4.98077i	2.44949			6.08450	−	3.46105i	−2.00000	+	2.00000i	2.59808	+	1.50000i	−1.22463	−	6.96421i
37.4	−1.36603	+	0.366025i	−1.67303	−	0.448288i	1.73205	−	1.00000i	4.98663	−	0.365451i	2.44949			−3.26382	−	6.19254i	−2.00000	+	2.00000i	2.59808	+	1.50000i	−6.67809	+	2.32445i
37.5	−1.36603	+	0.366025i	1.67303	+	0.448288i	1.73205	−	1.00000i	−4.60928	+	1.93765i	−2.44949			−1.45688	−	6.84672i	−2.00000	+	2.00000i	2.59808	+	1.50000i	5.58717	−	4.33400i
37.6	−1.36603	+	0.366025i	1.67303	+	0.448288i	1.73205	−	1.00000i	−2.69832	−	4.20940i	−2.44949			1.39786	+	6.85901i	−2.00000	+	2.00000i	2.59808	+	1.50000i	5.22672	+	4.76250i
37.7	−1.36603	+	0.366025i	1.67303	+	0.448288i	1.73205	−	1.00000i	2.01909	+	4.57420i	−2.44949			−6.19056	+	3.26756i	−2.00000	+	2.00000i	2.59808	+	1.50000i	−4.43240	−	5.50943i
37.8	−1.36603	+	0.366025i	1.67303	+	0.448288i	1.73205	−	1.00000i	4.87077	−	1.12941i	−2.44949			6.92053	−	1.05182i	−2.00000	+	2.00000i	2.59808	+	1.50000i	−6.24021	+	3.32563i
67.1	0.366025	−	1.36603i	−0.448288	−	1.67303i	−1.73205	−	1.00000i	−4.97092	−	0.538514i	−2.44949			3.26756	−	6.19056i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	−2.55510	+	6.59329i
67.2	0.366025	−	1.36603i	−0.448288	−	1.67303i	−1.73205	−	1.00000i	−1.45729	+	4.78292i	−2.44949			−1.05182	+	6.92053i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	6.00018	+	3.74136i
67.3	0.366025	−	1.36603i	−0.448288	−	1.67303i	−1.73205	−	1.00000i	0.626586	−	4.96058i	−2.44949			−6.84672	−	1.45688i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	−6.54694	−	2.67163i
67.4	0.366025	−	1.36603i	−0.448288	−	1.67303i	−1.73205	−	1.00000i	4.99461	−	0.232109i	−2.44949			6.85901	+	1.39786i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	1.51109	−	6.90772i
67.5	0.366025	−	1.36603i	0.448288	+	1.67303i	−1.73205	−	1.00000i	−4.09442	−	2.86979i	2.44949			−3.46105	+	6.08450i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	−5.41887	+	4.54267i
67.6	0.366025	−	1.36603i	0.448288	+	1.67303i	−1.73205	−	1.00000i	−2.17682	+	4.50127i	2.44949			−6.19254	−	3.26382i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	5.35208	+	4.62118i
67.7	0.366025	−	1.36603i	0.448288	+	1.67303i	−1.73205	−	1.00000i	3.99034	−	3.01284i	2.44949			−5.53495	−	4.28537i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	−2.65505	−	6.55368i
67.8	0.366025	−	1.36603i	0.448288	+	1.67303i	−1.73205	−	1.00000i	4.81996	+	1.32965i	2.44949			4.03230	+	5.72194i	−2.00000	+	2.00000i	−2.59808	+	1.50000i	3.58056	−	6.09751i
163.1	0.366025	+	1.36603i	−0.448288	+	1.67303i	−1.73205	+	1.00000i	−4.97092	+	0.538514i	−2.44949			3.26756	+	6.19056i	−2.00000	−	2.00000i	−2.59808	−	1.50000i	−2.55510	−	6.59329i
163.2	0.366025	+	1.36603i	−0.448288	+	1.67303i	−1.73205	+	1.00000i	−1.45729	−	4.78292i	−2.44949			−1.05182	−	6.92053i	−2.00000	−	2.00000i	−2.59808	−	1.50000i	6.00018	−	3.74136i
163.3	0.366025	+	1.36603i	−0.448288	+	1.67303i	−1.73205	+	1.00000i	0.626586	+	4.96058i	−2.44949			−6.84672	+	1.45688i	−2.00000	−	2.00000i	−2.59808	−	1.50000i	−6.54694	+	2.67163i
163.4	0.366025	+	1.36603i	−0.448288	+	1.67303i	−1.73205	+	1.00000i	4.99461	+	0.232109i	−2.44949			6.85901	−	1.39786i	−2.00000	−	2.00000i	−2.59808	−	1.50000i	1.51109	+	6.90772i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.c	even	3	1	inner
35.l	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	210.3.v.a	✓	32
5.c	odd	4	1	inner	210.3.v.a	✓	32
7.c	even	3	1	inner	210.3.v.a	✓	32
35.l	odd	12	1	inner	210.3.v.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.3.v.a	✓	32	1.a	even	1	1	trivial
210.3.v.a	✓	32	5.c	odd	4	1	inner
210.3.v.a	✓	32	7.c	even	3	1	inner
210.3.v.a	✓	32	35.l	odd	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T11^16 + 16*T11^15 + 646*T11^14 + 8632*T11^13 + 246126*T11^12 + 2951992*T11^11 + 54655792*T11^10 + 488427372*T11^9 + 7095961438*T11^8 + 51124314648*T11^7 + 574189235972*T11^6 + 2179220427768*T11^5 + 15703284237320*T11^4 - 14595269156008*T11^3 + 240995495480804*T11^2 + 89693218771080*T11 + 34757981448100