Newform orbit 154.3.p.a

• Label: 154.3.p.a
• Level: $154$
• Weight: $3$
• Character orbit: 154.p
• Analytic conductor: $4.196$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	154.p (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.19619607115\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(16\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 32 q^{4} - 4 q^{5} + 30 q^{7} + 60 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
39.1	−1.05097	−	0.946294i	−5.29618	+	2.35801i	0.209057	+	1.98904i	−8.30734	+	1.76578i	7.79748	+	2.53355i	−1.15738	+	6.90366i	1.66251	−	2.28825i	16.4672	−	18.2886i	10.4017	+	6.00541i
39.2	−1.05097	−	0.946294i	−3.15473	+	1.40458i	0.209057	+	1.98904i	2.21131	−	0.470028i	4.64465	+	1.50914i	3.86673	−	5.83510i	1.66251	−	2.28825i	1.95731	−	2.17381i	−2.76879	−	1.59856i
39.3	−1.05097	−	0.946294i	−1.61796	+	0.720360i	0.209057	+	1.98904i	−3.82771	+	0.813606i	2.38209	+	0.773987i	5.83594	−	3.86546i	1.66251	−	2.28825i	−3.92331	+	4.35728i	4.79271	+	2.76707i
39.4	−1.05097	−	0.946294i	−0.539899	+	0.240379i	0.209057	+	1.98904i	0.882910	−	0.187668i	0.794884	+	0.258274i	−6.95247	−	0.814387i	1.66251	−	2.28825i	−5.78847	+	6.42874i	−1.10550	−	0.638259i
39.5	−1.05097	−	0.946294i	0.244111	−	0.108685i	0.209057	+	1.98904i	7.66948	−	1.63020i	−0.359400	−	0.116776i	1.40863	+	6.85680i	1.66251	−	2.28825i	−5.97440	+	6.63524i	−9.60300	−	5.54429i
39.6	−1.05097	−	0.946294i	1.48827	−	0.662622i	0.209057	+	1.98904i	−4.70913	+	1.00096i	−2.19116	−	0.711951i	−1.34077	+	6.87040i	1.66251	−	2.28825i	−4.24629	+	4.71598i	5.89633	+	3.40425i
39.7	−1.05097	−	0.946294i	3.73256	−	1.66184i	0.209057	+	1.98904i	4.57160	−	0.971724i	−5.49538	−	1.78556i	−3.02746	−	6.31145i	1.66251	−	2.28825i	5.14808	−	5.71753i	−5.72413	−	3.30483i
39.8	−1.05097	−	0.946294i	5.14383	−	2.29018i	0.209057	+	1.98904i	−3.32614	+	0.706992i	−7.57317	−	2.46067i	6.05022	+	3.52064i	1.66251	−	2.28825i	15.1919	−	16.8723i	4.16468	+	2.40448i
39.9	1.05097	+	0.946294i	−4.53696	+	2.01998i	0.209057	+	1.98904i	−1.49874	+	0.318566i	−6.67969	−	2.17036i	−4.79000	−	5.10450i	−1.66251	+	2.28825i	10.4815	−	11.6409i	−1.87658	−	1.08344i
39.10	1.05097	+	0.946294i	−3.54170	+	1.57686i	0.209057	+	1.98904i	4.72709	−	1.00477i	−5.21438	−	1.69425i	−1.14894	+	6.90507i	−1.66251	+	2.28825i	4.03493	−	4.48125i	5.91882	+	3.41723i
39.11	1.05097	+	0.946294i	−1.46764	+	0.653436i	0.209057	+	1.98904i	6.58186	−	1.39902i	−2.16078	−	0.702081i	5.00410	−	4.89479i	−1.66251	+	2.28825i	−4.29518	+	4.77028i	8.24119	+	4.75805i
39.12	1.05097	+	0.946294i	−0.754996	+	0.336146i	0.209057	+	1.98904i	−9.41244	+	2.00068i	−1.11157	−	0.361170i	6.91397	−	1.09411i	−1.66251	+	2.28825i	−5.56515	+	6.18073i	−11.7854	−	6.80429i
39.13	1.05097	+	0.946294i	−0.191763	+	0.0853785i	0.209057	+	1.98904i	−4.89960	+	1.04144i	−0.282330	−	0.0917345i	−6.46926	+	2.67370i	−1.66251	+	2.28825i	−5.99269	+	6.65556i	−6.13482	−	3.54194i
39.14	1.05097	+	0.946294i	2.36523	−	1.05307i	0.209057	+	1.98904i	1.66857	−	0.354666i	3.48229	+	1.13146i	2.35260	+	6.59282i	−1.66251	+	2.28825i	−1.53681	+	1.70681i	2.08923	+	1.20622i
39.15	1.05097	+	0.946294i	3.85989	−	1.71853i	0.209057	+	1.98904i	7.10083	−	1.50933i	5.68285	+	1.84647i	−6.77043	−	1.77801i	−1.66251	+	2.28825i	5.92320	−	6.57838i	8.89100	+	5.13322i
39.16	1.05097	+	0.946294i	4.26794	−	1.90021i	0.209057	+	1.98904i	−2.59790	+	0.552201i	6.28361	+	2.04167i	4.92241	−	4.97693i	−1.66251	+	2.28825i	8.58234	−	9.53165i	−3.25285	−	1.87803i
51.1	−0.575212	−	1.29195i	−4.86226	+	1.03350i	−1.33826	+	1.48629i	0.191931	+	1.82610i	4.13207	+	5.68730i	−6.80456	−	1.64256i	2.68999	+	0.874032i	14.3515	−	6.38970i	2.24883	−	1.29836i
51.2	−0.575212	−	1.29195i	−3.72586	+	0.791956i	−1.33826	+	1.48629i	0.0539446	+	0.513249i	3.16633	+	4.35808i	6.78551	+	1.71956i	2.68999	+	0.874032i	5.03295	−	2.24081i	0.632061	−	0.364921i
51.3	−0.575212	−	1.29195i	−2.31573	+	0.492223i	−1.33826	+	1.48629i	−0.833966	−	7.93465i	1.96796	+	2.70867i	−1.61594	+	6.81093i	2.68999	+	0.874032i	−3.10159	+	1.38092i	−9.77146	+	5.64155i
51.4	−0.575212	−	1.29195i	−1.50800	+	0.320535i	−1.33826	+	1.48629i	0.0686064	+	0.652746i	1.28153	+	1.76388i	0.232252	−	6.99615i	2.68999	+	0.874032i	−6.05060	+	2.69390i	0.803851	−	0.464103i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
11.d	odd	10	1	inner
77.o	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	154.3.p.a	✓	128
7.c	even	3	1	inner	154.3.p.a	✓	128
11.d	odd	10	1	inner	154.3.p.a	✓	128
77.o	odd	30	1	inner	154.3.p.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
154.3.p.a	✓	128	1.a	even	1	1	trivial
154.3.p.a	✓	128	7.c	even	3	1	inner
154.3.p.a	✓	128	11.d	odd	10	1	inner
154.3.p.a	✓	128	77.o	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(154, [\chi])\).