Newform orbit 150.4.h.b

• Label: 150.4.h.b
• Level: $150$
• Weight: $4$
• Character orbit: 150.h
• Analytic conductor: $8.850$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.85028650086\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 32 q^{4} - 4 q^{5} + 48 q^{6} + 72 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.90211	+	0.618034i	−1.76336	−	2.42705i	3.23607	−	2.35114i	−10.8397	−	2.73870i	4.85410	+	3.52671i			21.3564i	−4.70228	+	6.47214i	−2.78115	+	8.55951i	22.3110	−	1.49000i
19.2	−1.90211	+	0.618034i	−1.76336	−	2.42705i	3.23607	−	2.35114i	−0.723135	+	11.1569i	4.85410	+	3.52671i		−	10.2336i	−4.70228	+	6.47214i	−2.78115	+	8.55951i	−5.51988	−	21.6687i
19.3	−1.90211	+	0.618034i	−1.76336	−	2.42705i	3.23607	−	2.35114i	0.944407	−	11.1404i	4.85410	+	3.52671i		−	22.9320i	−4.70228	+	6.47214i	−2.78115	+	8.55951i	5.08877	+	21.7739i
19.4	−1.90211	+	0.618034i	−1.76336	−	2.42705i	3.23607	−	2.35114i	11.0684	+	1.57808i	4.85410	+	3.52671i			6.77595i	−4.70228	+	6.47214i	−2.78115	+	8.55951i	−22.0287	+	3.83896i
19.5	1.90211	−	0.618034i	1.76336	+	2.42705i	3.23607	−	2.35114i	−10.0590	+	4.88023i	4.85410	+	3.52671i			12.9594i	4.70228	−	6.47214i	−2.78115	+	8.55951i	−16.1172	+	15.4996i
19.6	1.90211	−	0.618034i	1.76336	+	2.42705i	3.23607	−	2.35114i	−6.52419	−	9.07937i	4.85410	+	3.52671i		−	35.3218i	4.70228	−	6.47214i	−2.78115	+	8.55951i	−18.0211	−	13.2378i
19.7	1.90211	−	0.618034i	1.76336	+	2.42705i	3.23607	−	2.35114i	10.6920	+	3.26814i	4.85410	+	3.52671i		−	26.5168i	4.70228	−	6.47214i	−2.78115	+	8.55951i	22.3572	−	0.391659i
19.8	1.90211	−	0.618034i	1.76336	+	2.42705i	3.23607	−	2.35114i	11.1494	−	0.831106i	4.85410	+	3.52671i			29.8459i	4.70228	−	6.47214i	−2.78115	+	8.55951i	20.6938	−	8.47157i
79.1	−1.90211	−	0.618034i	−1.76336	+	2.42705i	3.23607	+	2.35114i	−10.8397	+	2.73870i	4.85410	−	3.52671i		−	21.3564i	−4.70228	−	6.47214i	−2.78115	−	8.55951i	22.3110	+	1.49000i
79.2	−1.90211	−	0.618034i	−1.76336	+	2.42705i	3.23607	+	2.35114i	−0.723135	−	11.1569i	4.85410	−	3.52671i			10.2336i	−4.70228	−	6.47214i	−2.78115	−	8.55951i	−5.51988	+	21.6687i
79.3	−1.90211	−	0.618034i	−1.76336	+	2.42705i	3.23607	+	2.35114i	0.944407	+	11.1404i	4.85410	−	3.52671i			22.9320i	−4.70228	−	6.47214i	−2.78115	−	8.55951i	5.08877	−	21.7739i
79.4	−1.90211	−	0.618034i	−1.76336	+	2.42705i	3.23607	+	2.35114i	11.0684	−	1.57808i	4.85410	−	3.52671i		−	6.77595i	−4.70228	−	6.47214i	−2.78115	−	8.55951i	−22.0287	−	3.83896i
79.5	1.90211	+	0.618034i	1.76336	−	2.42705i	3.23607	+	2.35114i	−10.0590	−	4.88023i	4.85410	−	3.52671i		−	12.9594i	4.70228	+	6.47214i	−2.78115	−	8.55951i	−16.1172	−	15.4996i
79.6	1.90211	+	0.618034i	1.76336	−	2.42705i	3.23607	+	2.35114i	−6.52419	+	9.07937i	4.85410	−	3.52671i			35.3218i	4.70228	+	6.47214i	−2.78115	−	8.55951i	−18.0211	+	13.2378i
79.7	1.90211	+	0.618034i	1.76336	−	2.42705i	3.23607	+	2.35114i	10.6920	−	3.26814i	4.85410	−	3.52671i			26.5168i	4.70228	+	6.47214i	−2.78115	−	8.55951i	22.3572	+	0.391659i
79.8	1.90211	+	0.618034i	1.76336	−	2.42705i	3.23607	+	2.35114i	11.1494	+	0.831106i	4.85410	−	3.52671i		−	29.8459i	4.70228	+	6.47214i	−2.78115	−	8.55951i	20.6938	+	8.47157i
109.1	−1.17557	+	1.61803i	2.85317	−	0.927051i	−1.23607	−	3.80423i	−11.1244	+	1.11657i	−1.85410	+	5.70634i		−	8.23614i	7.60845	+	2.47214i	7.28115	−	5.29007i	11.2709	−	19.3123i
109.2	−1.17557	+	1.61803i	2.85317	−	0.927051i	−1.23607	−	3.80423i	−4.70432	−	10.1425i	−1.85410	+	5.70634i			11.8707i	7.60845	+	2.47214i	7.28115	−	5.29007i	21.9411	+	4.31142i
109.3	−1.17557	+	1.61803i	2.85317	−	0.927051i	−1.23607	−	3.80423i	−4.38365	+	10.2851i	−1.85410	+	5.70634i			12.8965i	7.60845	+	2.47214i	7.28115	−	5.29007i	−11.4884	−	19.1838i
109.4	−1.17557	+	1.61803i	2.85317	−	0.927051i	−1.23607	−	3.80423i	9.61516	+	5.70515i	−1.85410	+	5.70634i		−	34.4948i	7.60845	+	2.47214i	7.28115	−	5.29007i	−20.5344	+	8.85084i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	150.4.h.b	✓	32
25.e	even	10	1	inner	150.4.h.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
150.4.h.b	✓	32	1.a	even	1	1	trivial
150.4.h.b	✓	32	25.e	even	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^32 + 6634*T7^30 + 19360575*T7^28 + 32849342400*T7^26 + 36103743127775*T7^24 + 27127550792002922*T7^22 + 14347923509475231823*T7^20 + 5425639593920225437350*T7^18 + 1477017530621338470622450*T7^16 + 289522946058543696425356450*T7^14 + 40597545201565209434841574028*T7^12 + 4011182400381305807016927541952*T7^10 + 271631488889417230824994425205825*T7^8 + 12008310868877215198600376266541400*T7^6 + 316689006570675000947026705308171400*T7^4 + 4096944618614188376476306403617187424*T7^2 + 13505913351242214273942080668158355216