Newform orbit 798.2.bn.a

• Label: 798.2.bn.a
• Level: $798$
• Weight: $2$
• Character orbit: 798.bn
• Analytic conductor: $6.372$
• Analytic rank: $0$
• Dimension: $104$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bn (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.37206208130\)
Analytic rank:	\(0\)
Dimension:	\(104\)
Relative dimension:	\(52\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 104 q - 104 q^{4} + 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
353.1		−	1.00000i	−1.73204	−	0.00585950i	−1.00000			−4.37911			−0.00585950	+	1.73204i	0.628400	+	2.57004i			1.00000i	2.99993	+	0.0202978i			4.37911i
353.2		−	1.00000i	−1.72691	−	0.133385i	−1.00000			−1.16969			−0.133385	+	1.72691i	1.51443	−	2.16945i			1.00000i	2.96442	+	0.460686i			1.16969i
353.3		−	1.00000i	−1.69417	+	0.360266i	−1.00000			2.41068			0.360266	+	1.69417i	−0.685369	+	2.55544i			1.00000i	2.74042	−	1.22070i		−	2.41068i
353.4		−	1.00000i	−1.55788	−	0.756982i	−1.00000			1.16693			−0.756982	+	1.55788i	2.56527	−	0.647587i			1.00000i	1.85396	+	2.35857i		−	1.16693i
353.5		−	1.00000i	−1.35308	+	1.08129i	−1.00000			−0.762444			1.08129	+	1.35308i	−1.80713	+	1.93243i			1.00000i	0.661629	−	2.92613i			0.762444i
353.6		−	1.00000i	−1.32484	−	1.11571i	−1.00000			−0.643570			−1.11571	+	1.32484i	−2.56463	+	0.650129i			1.00000i	0.510382	+	2.95627i			0.643570i
353.7		−	1.00000i	−1.30076	+	1.14368i	−1.00000			2.71103			1.14368	+	1.30076i	−0.331641	−	2.62488i			1.00000i	0.383975	−	2.97533i		−	2.71103i
353.8		−	1.00000i	−1.07098	−	1.36125i	−1.00000			0.832050			−1.36125	+	1.07098i	2.33836	+	1.23778i			1.00000i	−0.706011	+	2.91574i		−	0.832050i
353.9		−	1.00000i	−0.793943	+	1.53937i	−1.00000			2.69032			1.53937	+	0.793943i	2.56411	+	0.652194i			1.00000i	−1.73931	−	2.44434i		−	2.69032i
353.10		−	1.00000i	−0.489477	+	1.66145i	−1.00000			−0.944872			1.66145	+	0.489477i	−1.90711	+	1.83383i			1.00000i	−2.52082	−	1.62648i			0.944872i
353.11		−	1.00000i	−0.430346	−	1.67774i	−1.00000			−2.67848			−1.67774	+	0.430346i	−0.358506	−	2.62135i			1.00000i	−2.62960	+	1.44402i			2.67848i
353.12		−	1.00000i	−0.108104	+	1.72867i	−1.00000			0.727709			1.72867	+	0.108104i	−0.240912	−	2.63476i			1.00000i	−2.97663	−	0.373752i		−	0.727709i
353.13		−	1.00000i	−0.0205068	+	1.73193i	−1.00000			−3.93794			1.73193	+	0.0205068i	2.35858	−	1.19879i			1.00000i	−2.99916	−	0.0710327i			3.93794i
353.14		−	1.00000i	0.0633882	−	1.73089i	−1.00000			3.40287			−1.73089	−	0.0633882i	0.463625	−	2.60481i			1.00000i	−2.99196	−	0.219436i		−	3.40287i
353.15		−	1.00000i	0.0897714	−	1.72972i	−1.00000			−3.08108			−1.72972	−	0.0897714i	1.45255	+	2.21136i			1.00000i	−2.98388	−	0.310559i			3.08108i
353.16		−	1.00000i	0.184140	−	1.72223i	−1.00000			0.955808			−1.72223	−	0.184140i	−2.47443	+	0.936600i			1.00000i	−2.93218	−	0.634265i		−	0.955808i
353.17		−	1.00000i	0.723368	+	1.57377i	−1.00000			3.98517			1.57377	−	0.723368i	−2.62742	+	0.310875i			1.00000i	−1.95348	+	2.27682i		−	3.98517i
353.18		−	1.00000i	1.06101	+	1.36904i	−1.00000			−1.31153			1.36904	−	1.06101i	1.41291	+	2.23689i			1.00000i	−0.748518	+	2.90512i			1.31153i
353.19		−	1.00000i	1.12224	−	1.31931i	−1.00000			−0.550885			−1.31931	−	1.12224i	1.78801	+	1.95013i			1.00000i	−0.481156	−	2.96116i			0.550885i
353.20		−	1.00000i	1.22600	+	1.22349i	−1.00000			−0.764014			1.22349	−	1.22600i	−2.38978	−	1.13532i			1.00000i	0.00614135	+	2.99999i			0.764014i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
133.t	odd	6	1	inner
399.p	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	798.2.bn.a	yes	104
3.b	odd	2	1	inner	798.2.bn.a	yes	104
7.d	odd	6	1		798.2.w.a	✓	104
19.c	even	3	1		798.2.w.a	✓	104
21.g	even	6	1		798.2.w.a	✓	104
57.h	odd	6	1		798.2.w.a	✓	104
133.t	odd	6	1	inner	798.2.bn.a	yes	104
399.p	even	6	1	inner	798.2.bn.a	yes	104

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
798.2.w.a	✓	104	7.d	odd	6	1
798.2.w.a	✓	104	19.c	even	3	1
798.2.w.a	✓	104	21.g	even	6	1
798.2.w.a	✓	104	57.h	odd	6	1
798.2.bn.a	yes	104	1.a	even	1	1	trivial
798.2.bn.a	yes	104	3.b	odd	2	1	inner
798.2.bn.a	yes	104	133.t	odd	6	1	inner
798.2.bn.a	yes	104	399.p	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(798, [\chi])\).