Newform orbit 230.4.j.a

• Label: 230.4.j.a
• Level: $230$
• Weight: $4$
• Character orbit: 230.j
• Analytic conductor: $13.570$
• Analytic rank: $0$
• Dimension: $360$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.5704393013\)
Analytic rank:	\(0\)
Dimension:	\(360\)
Relative dimension:	\(36\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 360 * q + 144 * q^4 + 32 * q^5 + 8 * q^6 + 224 * q^9 + 96 * q^11 + 208 * q^14 - 752 * q^15 - 576 * q^16 + 48 * q^19 + 224 * q^20 - 272 * q^21 - 32 * q^24 + 904 * q^25 - 152 * q^26 - 20 * q^29 - 1272 * q^30 + 160 * q^31 + 128 * q^34 - 364 * q^35 - 896 * q^36 - 1476 * q^39 + 216 * q^41 - 384 * q^44 - 820 * q^45 + 416 * q^46 + 3814 * q^49 + 1000 * q^50 + 296 * q^51 - 2772 * q^54 - 4272 * q^55 + 1104 * q^56 - 6250 * q^59 - 72 * q^60 + 96 * q^61 + 2304 * q^64 + 8708 * q^65 - 6144 * q^66 + 14176 * q^69 + 6136 * q^70 - 11144 * q^71 + 4944 * q^74 + 6722 * q^75 - 192 * q^76 - 2680 * q^79 - 896 * q^80 + 4820 * q^81 - 2696 * q^84 - 7290 * q^85 + 2900 * q^86 + 880 * q^89 - 1104 * q^90 + 5272 * q^91 + 864 * q^94 + 7456 * q^95 + 128 * q^96 + 23448 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1	−0.563465	−	1.91899i	−7.34353	+	6.36321i	−3.36501	+	2.16256i	−7.26047	−	8.50209i	16.3487	+	10.5067i	−18.7911	−	8.58160i	6.04600	+	5.23889i	9.59456	−	66.7316i	−12.2244	+	18.7234i
9.2	−0.563465	−	1.91899i	−6.85739	+	5.94196i	−3.36501	+	2.16256i	11.1057	−	1.29006i	15.2664	+	9.81115i	9.56919	+	4.37010i	6.04600	+	5.23889i	7.87438	−	54.7675i	−8.73326	−	20.5847i
9.3	−0.563465	−	1.91899i	−6.12185	+	5.30461i	−3.36501	+	2.16256i	−10.8097	+	2.85485i	13.6289	+	8.75878i	32.7383	+	14.9511i	6.04600	+	5.23889i	5.49562	−	38.2229i	11.5693	+	19.1351i
9.4	−0.563465	−	1.91899i	−4.91203	+	4.25629i	−3.36501	+	2.16256i	6.66177	+	8.97891i	10.9355	+	7.02783i	−6.13831	−	2.80327i	6.04600	+	5.23889i	2.16945	−	15.0889i	13.4767	−	17.8432i
9.5	−0.563465	−	1.91899i	−4.12395	+	3.57342i	−3.36501	+	2.16256i	9.20079	−	6.35181i	9.18104	+	5.90030i	−12.3150	−	5.62406i	6.04600	+	5.23889i	0.395105	−	2.74801i	−17.3734	−	14.0772i
9.6	−0.563465	−	1.91899i	−3.19029	+	2.76440i	−3.36501	+	2.16256i	−9.29353	+	6.21533i	7.10247	+	4.56448i	−18.3244	−	8.36846i	6.04600	+	5.23889i	−1.30647	+	9.08669i	17.1637	+	14.3320i
9.7	−0.563465	−	1.91899i	−3.14614	+	2.72615i	−3.36501	+	2.16256i	−3.36640	−	10.6615i	7.00418	+	4.50131i	17.7210	+	8.09292i	6.04600	+	5.23889i	−1.37617	+	9.57148i	−18.5624	+	12.4675i
9.8	−0.563465	−	1.91899i	−2.50934	+	2.17435i	−3.36501	+	2.16256i	0.326731	+	11.1756i	5.58647	+	3.59021i	12.0046	+	5.48233i	6.04600	+	5.23889i	−2.27354	+	15.8128i	21.2617	−	6.92403i
9.9	−0.563465	−	1.91899i	0.694762	−	0.602015i	−3.36501	+	2.16256i	4.50572	−	10.2322i	−1.54673	−	0.994024i	−24.3344	−	11.1132i	6.04600	+	5.23889i	−3.72223	+	25.8887i	−22.1743	−	2.88090i
9.10	−0.563465	−	1.91899i	0.729490	−	0.632107i	−3.36501	+	2.16256i	−6.36706	−	9.19024i	−1.62405	−	1.04371i	6.54228	+	2.98776i	6.04600	+	5.23889i	−3.70990	+	25.8029i	−14.0483	+	17.3967i
9.11	−0.563465	−	1.91899i	1.26527	−	1.09636i	−3.36501	+	2.16256i	9.80304	+	5.37592i	−2.81684	−	1.81027i	20.0538	+	9.15826i	6.04600	+	5.23889i	−3.44360	+	23.9508i	4.79264	−	21.8410i
9.12	−0.563465	−	1.91899i	2.02304	−	1.75298i	−3.36501	+	2.16256i	−11.1730	−	0.405517i	−4.50385	−	2.89445i	8.71258	+	3.97890i	6.04600	+	5.23889i	−2.82272	+	19.6325i	5.51741	+	21.6693i
9.13	−0.563465	−	1.91899i	2.50028	−	2.16650i	−3.36501	+	2.16256i	8.44207	+	7.33017i	−5.56631	−	3.57725i	−13.3837	−	6.11215i	6.04600	+	5.23889i	−2.28485	+	15.8915i	9.30968	−	20.3305i
9.14	−0.563465	−	1.91899i	4.45429	−	3.85967i	−3.36501	+	2.16256i	7.13469	−	8.60792i	−9.91648	−	6.37294i	21.1421	+	9.65527i	6.04600	+	5.23889i	1.10120	−	7.65898i	−20.5386	−	8.84110i
9.15	−0.563465	−	1.91899i	4.68867	−	4.06275i	−3.36501	+	2.16256i	−10.9539	+	2.23870i	−10.4383	−	6.70826i	0.432083	+	0.197326i	6.04600	+	5.23889i	1.63513	−	11.3726i	10.4682	+	19.7590i
9.16	−0.563465	−	1.91899i	6.02364	−	5.21951i	−3.36501	+	2.16256i	10.3489	−	4.23080i	−13.4103	−	8.61826i	−6.46040	−	2.95037i	6.04600	+	5.23889i	5.19840	−	36.1557i	−13.9501	−	17.4755i
9.17	−0.563465	−	1.91899i	6.71164	−	5.81567i	−3.36501	+	2.16256i	−2.68913	+	10.8521i	−14.9420	−	9.60261i	25.7501	+	11.7597i	6.04600	+	5.23889i	7.38159	−	51.3401i	22.3403	−	0.954398i
9.18	−0.563465	−	1.91899i	7.66317	−	6.64017i	−3.36501	+	2.16256i	−7.45417	−	8.33278i	−17.0603	−	10.9640i	−22.8813	−	10.4496i	6.04600	+	5.23889i	10.7897	−	75.0443i	−11.7903	+	18.9997i
9.19	0.563465	+	1.91899i	−7.66317	+	6.64017i	−3.36501	+	2.16256i	4.80461	−	10.0953i	−17.0603	−	10.9640i	22.8813	+	10.4496i	−6.04600	−	5.23889i	10.7897	−	75.0443i	22.0800	+	3.53161i
9.20	0.563465	+	1.91899i	−6.71164	+	5.81567i	−3.36501	+	2.16256i	5.63759	+	9.65492i	−14.9420	−	9.60261i	−25.7501	−	11.7597i	−6.04600	−	5.23889i	7.38159	−	51.3401i	−15.3511	+	16.2587i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
23.c	even	11	1	inner
115.j	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	230.4.j.a	✓	360
5.b	even	2	1	inner	230.4.j.a	✓	360
23.c	even	11	1	inner	230.4.j.a	✓	360
115.j	even	22	1	inner	230.4.j.a	✓	360

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.4.j.a	✓	360	1.a	even	1	1	trivial
230.4.j.a	✓	360	5.b	even	2	1	inner
230.4.j.a	✓	360	23.c	even	11	1	inner
230.4.j.a	✓	360	115.j	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(230, [\chi])\).