Newform orbit 230.3.h.a

• Label: 230.3.h.a
• Level: $230$
• Weight: $3$
• Character orbit: 230.h
• Analytic conductor: $6.267$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.h (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.26704608029\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(16\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 32 q^{4} + 8 q^{6} - 64 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.18971	+	0.764582i	−0.742007	+	5.16077i	0.830830	−	1.81926i	0.629973	+	2.14549i	−3.06306	−	6.70716i	−1.85848	+	1.61038i	0.402527	+	2.79964i	−17.4476	−	5.12306i	−2.38989	−	2.07085i
11.2	−1.18971	+	0.764582i	−0.599652	+	4.17067i	0.830830	−	1.81926i	−0.629973	−	2.14549i	−2.47540	−	5.42038i	7.86181	−	6.81230i	0.402527	+	2.79964i	−8.39947	−	2.46631i	2.38989	+	2.07085i
11.3	−1.18971	+	0.764582i	−0.327575	+	2.27833i	0.830830	−	1.81926i	−0.629973	−	2.14549i	−1.35225	−	2.96102i	−0.539945	+	0.467865i	0.402527	+	2.79964i	3.55194	+	1.04294i	2.38989	+	2.07085i
11.4	−1.18971	+	0.764582i	−0.313308	+	2.17910i	0.830830	−	1.81926i	0.629973	+	2.14549i	−1.29336	−	2.83205i	6.86066	−	5.94479i	0.402527	+	2.79964i	3.98511	+	1.17013i	−2.38989	−	2.07085i
11.5	−1.18971	+	0.764582i	0.0795672	−	0.553402i	0.830830	−	1.81926i	−0.629973	−	2.14549i	0.328459	+	0.719224i	−4.47356	+	3.87637i	0.402527	+	2.79964i	8.33551	+	2.44753i	2.38989	+	2.07085i
11.6	−1.18971	+	0.764582i	0.435036	−	3.02574i	0.830830	−	1.81926i	−0.629973	−	2.14549i	1.79586	+	3.93239i	−1.41880	+	1.22940i	0.402527	+	2.79964i	−0.330439	−	0.0970257i	2.38989	+	2.07085i
11.7	−1.18971	+	0.764582i	0.441868	−	3.07326i	0.830830	−	1.81926i	0.629973	+	2.14549i	1.82406	+	3.99414i	5.59049	−	4.84419i	0.402527	+	2.79964i	−0.614241	−	0.180357i	−2.38989	−	2.07085i
11.8	−1.18971	+	0.764582i	0.687442	−	4.78127i	0.830830	−	1.81926i	0.629973	+	2.14549i	2.83781	+	6.21394i	−9.48706	+	8.22059i	0.402527	+	2.79964i	−13.7525	−	4.03810i	−2.38989	−	2.07085i
11.9	1.18971	−	0.764582i	−0.569175	+	3.95870i	0.830830	−	1.81926i	0.629973	+	2.14549i	2.34960	+	5.14490i	−5.33345	+	4.62146i	−0.402527	−	2.79964i	−6.71192	−	1.97080i	2.38989	+	2.07085i
11.10	1.18971	−	0.764582i	−0.562585	+	3.91286i	0.830830	−	1.81926i	−0.629973	−	2.14549i	2.32239	+	5.08532i	−10.0271	+	8.68857i	−0.402527	−	2.79964i	−6.35855	−	1.86704i	−2.38989	−	2.07085i
11.11	1.18971	−	0.764582i	−0.344239	+	2.39424i	0.830830	−	1.81926i	0.629973	+	2.14549i	1.42104	+	3.11165i	8.39517	−	7.27446i	−0.402527	−	2.79964i	3.02157	+	0.887212i	2.38989	+	2.07085i
11.12	1.18971	−	0.764582i	−0.204860	+	1.42483i	0.830830	−	1.81926i	−0.629973	−	2.14549i	0.845674	+	1.85177i	1.20247	−	1.04195i	−0.402527	−	2.79964i	6.64727	+	1.95181i	−2.38989	−	2.07085i
11.13	1.18971	−	0.764582i	0.130600	−	0.908344i	0.830830	−	1.81926i	0.629973	+	2.14549i	−0.539127	−	1.18052i	0.612141	−	0.530423i	−0.402527	−	2.79964i	7.82740	+	2.29833i	2.38989	+	2.07085i
11.14	1.18971	−	0.764582i	0.472631	−	3.28722i	0.830830	−	1.81926i	−0.629973	−	2.14549i	−1.95105	−	4.27221i	6.97097	−	6.04038i	−0.402527	−	2.79964i	−1.94701	−	0.571695i	−2.38989	−	2.07085i
11.15	1.18971	−	0.764582i	0.707436	−	4.92033i	0.830830	−	1.81926i	−0.629973	−	2.14549i	−2.92035	−	6.39466i	−8.64217	+	7.48848i	−0.402527	−	2.79964i	−15.0737	−	4.42604i	−2.38989	−	2.07085i
11.16	1.18971	−	0.764582i	0.708819	−	4.92994i	0.830830	−	1.81926i	0.629973	+	2.14549i	−2.92605	−	6.40716i	4.28691	−	3.71463i	−0.402527	−	2.79964i	−15.1665	−	4.45328i	2.38989	+	2.07085i
21.1	−1.18971	−	0.764582i	−0.742007	−	5.16077i	0.830830	+	1.81926i	0.629973	−	2.14549i	−3.06306	+	6.70716i	−1.85848	−	1.61038i	0.402527	−	2.79964i	−17.4476	+	5.12306i	−2.38989	+	2.07085i
21.2	−1.18971	−	0.764582i	−0.599652	−	4.17067i	0.830830	+	1.81926i	−0.629973	+	2.14549i	−2.47540	+	5.42038i	7.86181	+	6.81230i	0.402527	−	2.79964i	−8.39947	+	2.46631i	2.38989	−	2.07085i
21.3	−1.18971	−	0.764582i	−0.327575	−	2.27833i	0.830830	+	1.81926i	−0.629973	+	2.14549i	−1.35225	+	2.96102i	−0.539945	−	0.467865i	0.402527	−	2.79964i	3.55194	−	1.04294i	2.38989	−	2.07085i
21.4	−1.18971	−	0.764582i	−0.313308	−	2.17910i	0.830830	+	1.81926i	0.629973	−	2.14549i	−1.29336	+	2.83205i	6.86066	+	5.94479i	0.402527	−	2.79964i	3.98511	−	1.17013i	−2.38989	+	2.07085i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.d	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	230.3.h.a	✓	160
23.d	odd	22	1	inner	230.3.h.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.3.h.a	✓	160	1.a	even	1	1	trivial
230.3.h.a	✓	160	23.d	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(230, [\chi])\).