Newform orbit 114.3.k.a

• Label: 114.3.k.a
• Level: $114$
• Weight: $3$
• Character orbit: 114.k
• Analytic conductor: $3.106$
• Analytic rank: $0$
• Dimension: $84$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	114.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.10627501371\)
Analytic rank:	\(0\)
Dimension:	\(84\)
Relative dimension:	\(14\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 84 q + 6 q^{3} - 12 q^{6} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−0.483690	−	1.32893i	−2.88947	−	0.806808i	−1.53209	+	1.28558i	−1.76037	+	2.09793i	0.325421	+	4.23014i	2.58777	+	4.48215i	2.44949	+	1.41421i	7.69812	+	4.66250i	3.63946	+	1.32466i
5.2	−0.483690	−	1.32893i	−2.29211	+	1.93552i	−1.53209	+	1.28558i	2.97202	−	3.54192i	3.68083	+	2.10986i	−1.58610	−	2.74721i	2.44949	+	1.41421i	1.50754	−	8.87284i	−6.14448	−	2.23641i
5.3	−0.483690	−	1.32893i	0.0809891	−	2.99891i	−1.53209	+	1.28558i	−3.63317	+	4.32984i	−4.02450	+	1.34291i	−4.68401	−	8.11293i	2.44949	+	1.41421i	−8.98688	−	0.485758i	7.51136	+	2.73391i
5.4	−0.483690	−	1.32893i	0.555457	+	2.94813i	−1.53209	+	1.28558i	1.34396	−	1.60167i	3.64918	−	2.16414i	2.11203	+	3.65814i	2.44949	+	1.41421i	−8.38294	+	3.27512i	−2.77856	−	1.01131i
5.5	−0.483690	−	1.32893i	1.55988	−	2.56257i	−1.53209	+	1.28558i	5.31349	−	6.33237i	−4.15997	−	0.833471i	4.61948	+	8.00117i	2.44949	+	1.41421i	−4.13357	−	7.99460i	−10.9853	−	3.99833i
5.6	−0.483690	−	1.32893i	2.95719	+	0.505005i	−1.53209	+	1.28558i	−5.47600	+	6.52605i	−0.759247	−	4.17415i	6.07385	+	10.5202i	2.44949	+	1.41421i	8.48994	+	2.98679i	11.3213	+	4.12062i
5.7	−0.483690	−	1.32893i	2.97190	−	0.409667i	−1.53209	+	1.28558i	1.24007	−	1.47786i	−1.98189	−	3.75128i	−5.53790	−	9.59192i	2.44949	+	1.41421i	8.66435	−	2.43498i	−2.56378	−	0.933139i
5.8	0.483690	+	1.32893i	−2.95157	−	0.536869i	−1.53209	+	1.28558i	5.47600	−	6.52605i	−0.714185	−	4.18210i	6.07385	+	10.5202i	−2.44949	−	1.41421i	8.42354	+	3.16921i	11.3213	+	4.12062i
5.9	0.483690	+	1.32893i	−2.65256	−	1.40141i	−1.53209	+	1.28558i	−1.24007	+	1.47786i	0.579357	−	4.20290i	−5.53790	−	9.59192i	−2.44949	−	1.41421i	5.07210	+	7.43463i	−2.56378	−	0.933139i
5.10	0.483690	+	1.32893i	−1.53028	+	2.58036i	−1.53209	+	1.28558i	−1.34396	+	1.60167i	−4.16928	−	0.785535i	2.11203	+	3.65814i	−2.44949	−	1.41421i	−4.31650	−	7.89733i	−2.77856	−	1.01131i
5.11	0.483690	+	1.32893i	−0.589353	−	2.94154i	−1.53209	+	1.28558i	−5.31349	+	6.33237i	3.62403	−	2.20600i	4.61948	+	8.00117i	−2.44949	−	1.41421i	−8.30533	+	3.46721i	−10.9853	−	3.99833i
5.12	0.483690	+	1.32893i	0.949582	−	2.84575i	−1.53209	+	1.28558i	3.63317	−	4.32984i	4.24109	−	0.114536i	−4.68401	−	8.11293i	−2.44949	−	1.41421i	−7.19659	−	5.40454i	7.51136	+	2.73391i
5.13	0.483690	+	1.32893i	1.49189	+	2.60274i	−1.53209	+	1.28558i	−2.97202	+	3.54192i	−2.73724	+	3.24153i	−1.58610	−	2.74721i	−2.44949	−	1.41421i	−4.54851	+	7.76602i	−6.14448	−	2.23641i
5.14	0.483690	+	1.32893i	2.99116	+	0.230107i	−1.53209	+	1.28558i	1.76037	−	2.09793i	1.14100	+	4.08633i	2.58777	+	4.48215i	−2.44949	−	1.41421i	8.89410	+	1.37658i	3.63946	+	1.32466i
17.1	−1.39273	−	0.245576i	−2.90528	+	0.747879i	1.87939	+	0.684040i	1.54011	+	4.23143i	4.22993	−	0.328125i	−3.13806	−	5.43528i	−2.44949	−	1.41421i	7.88135	−	4.34560i	−1.10582	−	6.27144i
17.2	−1.39273	−	0.245576i	−2.24350	+	1.99165i	1.87939	+	0.684040i	−2.04484	−	5.61816i	3.61369	−	2.22288i	2.32411	+	4.02547i	−2.44949	−	1.41421i	1.06663	−	8.93657i	1.46823	+	8.32674i
17.3	−1.39273	−	0.245576i	−1.06948	−	2.80289i	1.87939	+	0.684040i	−2.09797	−	5.76412i	0.801169	+	4.16631i	1.50451	+	2.60588i	−2.44949	−	1.41421i	−6.71244	+	5.99527i	1.50637	+	8.54307i
17.4	−1.39273	−	0.245576i	−0.722643	−	2.91166i	1.87939	+	0.684040i	3.15776	+	8.67589i	0.291411	+	4.23262i	−0.670969	−	1.16215i	−2.44949	−	1.41421i	−7.95558	+	4.20818i	−2.26732	−	12.8586i
17.5	−1.39273	−	0.245576i	0.656982	+	2.92718i	1.87939	+	0.684040i	1.21155	+	3.32870i	−0.196153	−	4.23810i	0.0547110	+	0.0947622i	−2.44949	−	1.41421i	−8.13675	+	3.84620i	−0.869910	−	4.93350i
17.6	−1.39273	−	0.245576i	2.81842	+	1.02786i	1.87939	+	0.684040i	−2.40229	−	6.60023i	−3.67288	−	2.12367i	−6.30005	−	10.9120i	−2.44949	−	1.41421i	6.88699	+	5.79391i	1.72488	+	9.78228i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
19.e	even	9	1	inner
57.l	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	114.3.k.a	✓	84
3.b	odd	2	1	inner	114.3.k.a	✓	84
19.e	even	9	1	inner	114.3.k.a	✓	84
57.l	odd	18	1	inner	114.3.k.a	✓	84

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
114.3.k.a	✓	84	1.a	even	1	1	trivial
114.3.k.a	✓	84	3.b	odd	2	1	inner
114.3.k.a	✓	84	19.e	even	9	1	inner
114.3.k.a	✓	84	57.l	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(114, [\chi])\).