Newform orbit 123.5.h.a

• Label: 123.5.h.a
• Level: $123$
• Weight: $5$
• Character orbit: 123.h
• Analytic conductor: $12.715$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	123.h (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.7145054593\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
55.1	−5.19792	−	5.19792i	1.98848	+	4.80062i			38.0368i	−9.05677	+	9.05677i	14.6173	−	35.2892i	−32.3727	−	78.1546i	114.546	−	114.546i	−19.0919	+	19.0919i	94.1528
55.2	−5.19190	−	5.19190i	−1.98848	−	4.80062i			37.9117i	10.0977	−	10.0977i	−14.6003	+	35.2484i	15.8757	+	38.3273i	113.764	−	113.764i	−19.0919	+	19.0919i	−104.852
55.3	−5.11875	−	5.11875i	1.98848	+	4.80062i			36.4033i	30.8958	−	30.8958i	14.3946	−	34.7517i	17.7071	+	42.7486i	104.439	−	104.439i	−19.0919	+	19.0919i	−316.296
55.4	−4.75673	−	4.75673i	1.98848	+	4.80062i			29.2529i	−29.0589	+	29.0589i	13.3766	−	32.2939i	27.1221	+	65.4786i	63.0405	−	63.0405i	−19.0919	+	19.0919i	276.451
55.5	−4.37741	−	4.37741i	−1.98848	−	4.80062i			22.3234i	2.56511	−	2.56511i	−12.3099	+	29.7186i	−19.6713	−	47.4908i	27.6800	−	27.6800i	−19.0919	+	19.0919i	−22.4571
55.6	−3.83887	−	3.83887i	1.98848	+	4.80062i			13.4738i	1.22599	−	1.22599i	10.7954	−	26.0625i	−4.31499	−	10.4173i	−9.69772	+	9.69772i	−19.0919	+	19.0919i	−9.41284
55.7	−3.78100	−	3.78100i	−1.98848	−	4.80062i			12.5919i	−29.4161	+	29.4161i	−10.6327	+	25.6696i	0.787577	+	1.90138i	−12.8861	+	12.8861i	−19.0919	+	19.0919i	222.444
55.8	−2.82966	−	2.82966i	−1.98848	−	4.80062i			0.0139976i	17.5997	−	17.5997i	−7.95740	+	19.2109i	27.9958	+	67.5878i	−45.2350	+	45.2350i	−19.0919	+	19.0919i	−99.6026
55.9	−2.43189	−	2.43189i	−1.98848	−	4.80062i		−	4.17183i	4.48532	−	4.48532i	−6.83881	+	16.5103i	−25.3014	−	61.0830i	−49.0557	+	49.0557i	−19.0919	+	19.0919i	−21.8156
55.10	−2.22261	−	2.22261i	1.98848	+	4.80062i		−	6.12003i	0.688772	−	0.688772i	6.25028	−	15.0895i	8.79729	+	21.2385i	−49.1641	+	49.1641i	−19.0919	+	19.0919i	−3.06174
55.11	−1.19262	−	1.19262i	1.98848	+	4.80062i		−	13.1553i	28.0173	−	28.0173i	3.35380	−	8.09679i	−23.4848	−	56.6973i	−34.7711	+	34.7711i	−19.0919	+	19.0919i	−66.8278
55.12	−0.937220	−	0.937220i	−1.98848	−	4.80062i		−	14.2432i	−14.2400	+	14.2400i	−2.63559	+	6.36288i	24.9312	+	60.1892i	−28.3446	+	28.3446i	−19.0919	+	19.0919i	26.6920
55.13	−0.482238	−	0.482238i	−1.98848	−	4.80062i		−	15.5349i	−10.1262	+	10.1262i	−1.35612	+	3.27396i	−22.1843	−	53.5576i	−15.2073	+	15.2073i	−19.0919	+	19.0919i	9.76647
55.14	−0.182194	−	0.182194i	1.98848	+	4.80062i		−	15.9336i	−28.3476	+	28.3476i	0.512353	−	1.23693i	0.370788	+	0.895161i	−5.81810	+	5.81810i	−19.0919	+	19.0919i	10.3295
55.15	0.602298	+	0.602298i	−1.98848	−	4.80062i		−	15.2745i	24.6585	−	24.6585i	1.69374	−	4.08906i	13.3025	+	32.1151i	18.8365	−	18.8365i	−19.0919	+	19.0919i	29.7035
55.16	1.09923	+	1.09923i	−1.98848	−	4.80062i		−	13.5834i	21.7988	−	21.7988i	3.09118	−	7.46276i	−16.8538	−	40.6888i	32.5189	−	32.5189i	−19.0919	+	19.0919i	47.9236
55.17	1.12812	+	1.12812i	1.98848	+	4.80062i		−	13.4547i	−13.0304	+	13.0304i	−3.17242	+	7.65890i	12.5643	+	30.3329i	33.2284	−	33.2284i	−19.0919	+	19.0919i	−29.3996
55.18	1.66535	+	1.66535i	−1.98848	−	4.80062i		−	10.4532i	−20.8931	+	20.8931i	4.68320	−	11.3062i	13.2733	+	32.0446i	44.0539	−	44.0539i	−19.0919	+	19.0919i	−69.5889
55.19	1.91562	+	1.91562i	1.98848	+	4.80062i		−	8.66078i	−7.82476	+	7.82476i	−5.38700	+	13.0054i	−29.1723	−	70.4281i	47.2408	−	47.2408i	−19.0919	+	19.0919i	−29.9786
55.20	2.25001	+	2.25001i	1.98848	+	4.80062i		−	5.87491i	4.31373	−	4.31373i	−6.32734	+	15.2755i	−0.920394	−	2.22203i	49.2188	−	49.2188i	−19.0919	+	19.0919i	19.4119

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.e	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	123.5.h.a	✓	112
41.e	odd	8	1	inner	123.5.h.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
123.5.h.a	✓	112	1.a	even	1	1	trivial
123.5.h.a	✓	112	41.e	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(123, [\chi])\).