Newform orbit 798.2.w.a

• Label: 798.2.w.a
• Level: $798$
• Weight: $2$
• Character orbit: 798.w
• 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.w (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.

\(\operatorname{Tr}(f)(q) = \) \( 104 q + 52 q^{4} + 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
311.1	−0.866025	−	0.500000i	−1.71437	−	0.246869i	0.500000	+	0.866025i	0.416025	−	0.720576i	1.36125	+	1.07098i	2.33836	+	1.23778i		−	1.00000i	2.87811	+	0.846447i	−0.720576	+	0.416025i
311.2	−0.866025	−	0.500000i	−1.66814	+	0.466178i	0.500000	+	0.866025i	−1.33924	+	2.31963i	1.67774	+	0.430346i	−0.358506	−	2.62135i		−	1.00000i	2.56536	−	1.55530i	2.31963	−	1.33924i
311.3	−0.866025	−	0.500000i	−1.62865	−	0.589487i	0.500000	+	0.866025i	−0.321785	+	0.557348i	1.11571	+	1.32484i	−2.56463	+	0.650129i		−	1.00000i	2.30501	+	1.92014i	0.557348	−	0.321785i
311.4	−0.866025	−	0.500000i	−1.46730	+	0.920341i	0.500000	+	0.866025i	1.70143	−	2.94697i	1.73089	−	0.0633882i	0.463625	−	2.60481i		−	1.00000i	1.30594	−	2.70083i	−2.94697	+	1.70143i
311.5	−0.866025	−	0.500000i	−1.45310	+	0.942606i	0.500000	+	0.866025i	−1.54054	+	2.66829i	1.72972	−	0.0897714i	1.45255	+	2.21136i		−	1.00000i	1.22299	−	2.73940i	2.66829	−	1.54054i
311.6	−0.866025	−	0.500000i	−1.43450	−	0.970669i	0.500000	+	0.866025i	0.583467	−	1.01059i	0.756982	+	1.55788i	2.56527	−	0.647587i		−	1.00000i	1.11560	+	2.78486i	−1.01059	+	0.583467i
311.7	−0.866025	−	0.500000i	−1.39943	+	1.02059i	0.500000	+	0.866025i	0.477904	−	0.827754i	1.72223	−	0.184140i	−2.47443	+	0.936600i		−	1.00000i	0.916803	−	2.85648i	−0.827754	+	0.477904i
311.8	−0.866025	−	0.500000i	−0.978968	−	1.42885i	0.500000	+	0.866025i	−0.584845	+	1.01298i	0.133385	+	1.72691i	1.51443	−	2.16945i		−	1.00000i	−1.08324	+	2.79760i	1.01298	−	0.584845i
311.9	−0.866025	−	0.500000i	−0.871095	−	1.49706i	0.500000	+	0.866025i	−2.18956	+	3.79242i	0.00585950	+	1.73204i	0.628400	+	2.57004i		−	1.00000i	−1.48239	+	2.60817i	3.79242	−	2.18956i
311.10	−0.866025	−	0.500000i	−0.581436	+	1.63154i	0.500000	+	0.866025i	−0.275442	+	0.477080i	1.31931	−	1.12224i	1.78801	+	1.95013i		−	1.00000i	−2.32386	−	1.89728i	0.477080	−	0.275442i
311.11	−0.866025	−	0.500000i	−0.535085	−	1.64733i	0.500000	+	0.866025i	1.20534	−	2.08771i	−0.360266	+	1.69417i	−0.685369	+	2.55544i		−	1.00000i	−2.42737	+	1.76292i	−2.08771	+	1.20534i
311.12	−0.866025	−	0.500000i	−0.322410	+	1.70178i	0.500000	+	0.866025i	0.540003	−	0.935313i	1.13010	−	1.31258i	−2.37817	−	1.15944i		−	1.00000i	−2.79210	−	1.09734i	−0.935313	+	0.540003i
311.13	−0.866025	−	0.500000i	−0.239660	+	1.71539i	0.500000	+	0.866025i	2.17399	−	3.76547i	1.06525	−	1.36574i	2.64176	+	0.145281i		−	1.00000i	−2.88513	−	0.822221i	−3.76547	+	2.17399i
311.14	−0.866025	−	0.500000i	−0.0273444	+	1.73183i	0.500000	+	0.866025i	−1.41848	+	2.45689i	0.889598	−	1.48614i	0.863523	−	2.50087i		−	1.00000i	−2.99850	−	0.0947118i	2.45689	−	1.41848i
311.15	−0.866025	−	0.500000i	0.259886	−	1.71244i	0.500000	+	0.866025i	−0.381222	+	0.660296i	−1.08129	+	1.35308i	−1.80713	+	1.93243i		−	1.00000i	−2.86492	−	0.890078i	0.660296	−	0.381222i
311.16	−0.866025	−	0.500000i	0.340077	−	1.69834i	0.500000	+	0.866025i	1.35551	−	2.34782i	−1.14368	+	1.30076i	−0.331641	−	2.62488i		−	1.00000i	−2.76870	−	1.15513i	−2.34782	+	1.35551i
311.17	−0.866025	−	0.500000i	0.883615	+	1.48971i	0.500000	+	0.866025i	0.967471	−	1.67571i	−0.0203795	−	1.73193i	−0.442197	+	2.60854i		−	1.00000i	−1.43845	+	2.63265i	−1.67571	+	0.967471i
311.18	−0.866025	−	0.500000i	0.936161	−	1.45726i	0.500000	+	0.866025i	1.34516	−	2.32988i	−1.53937	+	0.793943i	2.56411	+	0.652194i		−	1.00000i	−1.24721	−	2.72846i	−2.32988	+	1.34516i
311.19	−0.866025	−	0.500000i	1.19412	−	1.25462i	0.500000	+	0.866025i	−0.472436	+	0.818283i	−1.66145	+	0.489477i	−1.90711	+	1.83383i		−	1.00000i	−0.148162	−	2.99634i	0.818283	−	0.472436i
311.20	−0.866025	−	0.500000i	1.24513	+	1.20401i	0.500000	+	0.866025i	0.234081	−	0.405440i	−0.476310	−	1.66527i	2.09636	−	1.61409i		−	1.00000i	0.100708	+	2.99831i	−0.405440	+	0.234081i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
133.k	odd	6	1	inner
399.bd	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.w.a	✓	104
3.b	odd	2	1	inner	798.2.w.a	✓	104
7.d	odd	6	1		798.2.bn.a	yes	104
19.c	even	3	1		798.2.bn.a	yes	104
21.g	even	6	1		798.2.bn.a	yes	104
57.h	odd	6	1		798.2.bn.a	yes	104
133.k	odd	6	1	inner	798.2.w.a	✓	104
399.bd	even	6	1	inner	798.2.w.a	✓	104

    

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

Hecke kernels

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