Newform orbit 154.3.o.a

• Label: 154.3.o.a
• Level: $154$
• Weight: $3$
• Character orbit: 154.o
• 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.o (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.

\(\operatorname{Tr}(f)(q) = \) \( 128 q + 32 q^{4} + 12 q^{5} + 26 q^{7} - 60 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.29195	−	0.575212i	−0.946279	+	4.45189i	1.33826	+	1.48629i	−3.67523	−	0.386282i	3.78333	−	5.20730i	−4.45210	+	5.40174i	−0.874032	−	2.68999i	−10.7020	−	4.76483i	4.52602	+	2.61310i
3.2	−1.29195	−	0.575212i	−0.915871	+	4.30884i	1.33826	+	1.48629i	6.04629	+	0.635491i	3.66176	−	5.03997i	6.68929	+	2.06236i	−0.874032	−	2.68999i	−9.50534	−	4.23205i	−7.44596	−	4.29893i
3.3	−1.29195	−	0.575212i	−0.430954	+	2.02748i	1.33826	+	1.48629i	7.28778	+	0.765976i	1.72300	−	2.37151i	−6.06356	−	3.49760i	−0.874032	−	2.68999i	4.29696	+	1.91313i	−8.97483	−	5.18162i
3.4	−1.29195	−	0.575212i	−0.226499	+	1.06559i	1.33826	+	1.48629i	−8.21128	−	0.863040i	0.905567	−	1.24641i	5.10033	−	4.79444i	−0.874032	−	2.68999i	7.13772	+	3.17792i	10.1121	+	5.83823i
3.5	−1.29195	−	0.575212i	0.231234	−	1.08787i	1.33826	+	1.48629i	−4.58100	−	0.481482i	−0.924497	+	1.27246i	−0.933126	+	6.93753i	−0.874032	−	2.68999i	7.09192	+	3.15753i	5.64146	+	3.25710i
3.6	−1.29195	−	0.575212i	0.367452	−	1.72873i	1.33826	+	1.48629i	−0.640175	−	0.0672851i	−1.46911	+	2.02206i	−3.23602	−	6.20711i	−0.874032	−	2.68999i	5.36844	+	2.39018i	0.788370	+	0.455166i
3.7	−1.29195	−	0.575212i	0.751729	−	3.53661i	1.33826	+	1.48629i	5.71204	+	0.600359i	−3.00549	+	4.13671i	6.32172	−	3.00596i	−0.874032	−	2.68999i	−3.72057	−	1.65651i	−7.03432	−	4.06127i
3.8	−1.29195	−	0.575212i	1.16919	−	5.50060i	1.33826	+	1.48629i	−3.88497	−	0.408327i	−4.67455	+	6.43396i	−6.55673	+	2.45139i	−0.874032	−	2.68999i	−20.6677	−	9.20185i	4.78431	+	2.76222i
3.9	1.29195	+	0.575212i	−1.01971	+	4.79734i	1.33826	+	1.48629i	6.86700	+	0.721750i	−4.07689	+	5.61136i	5.60813	−	4.18914i	0.874032	+	2.68999i	−13.7527	−	6.12311i	8.45664	+	4.88245i
3.10	1.29195	+	0.575212i	−0.836678	+	3.93626i	1.33826	+	1.48629i	1.05382	+	0.110761i	−3.34513	+	4.60418i	−4.04675	+	5.71172i	0.874032	+	2.68999i	−6.57221	−	2.92614i	1.29777	+	0.749267i
3.11	1.29195	+	0.575212i	−0.665085	+	3.12898i	1.33826	+	1.48629i	−9.17324	−	0.964147i	−2.65908	+	3.65992i	−5.49569	−	4.33560i	0.874032	+	2.68999i	−1.12627	−	0.501449i	−11.2968	−	6.52219i
3.12	1.29195	+	0.575212i	−0.00134292	+	0.00631796i	1.33826	+	1.48629i	−2.87638	−	0.302320i	−0.00536916	+	0.00739001i	4.24467	+	5.56621i	0.874032	+	2.68999i	8.22187	+	3.66061i	−3.54224	−	2.04511i
3.13	1.29195	+	0.575212i	0.0738035	−	0.347218i	1.33826	+	1.48629i	2.86770	+	0.301407i	0.295075	−	0.406135i	2.60212	−	6.49838i	0.874032	+	2.68999i	8.10680	+	3.60938i	3.53155	+	2.03894i
3.14	1.29195	+	0.575212i	0.381228	−	1.79354i	1.33826	+	1.48629i	6.48043	+	0.681121i	1.52419	−	2.09787i	−6.93879	+	0.923659i	0.874032	+	2.68999i	5.15047	+	2.29314i	7.98060	+	4.60760i
3.15	1.29195	+	0.575212i	0.942442	−	4.43384i	1.33826	+	1.48629i	−6.44135	−	0.677013i	3.76799	−	5.18619i	1.32617	−	6.87323i	0.874032	+	2.68999i	−10.5488	−	4.69664i	−7.93246	−	4.57981i
3.16	1.29195	+	0.575212i	1.12534	−	5.29430i	1.33826	+	1.48629i	5.29777	+	0.556818i	4.49923	−	6.19265i	5.12680	+	4.76613i	0.874032	+	2.68999i	−18.5413	−	8.25513i	6.52416	+	3.76673i
5.1	−1.38331	−	0.294032i	−5.60792	−	0.589416i	1.82709	+	0.813473i	4.47415	−	4.02854i	7.58418	+	2.46425i	−0.104577	−	6.99922i	−2.28825	−	1.66251i	22.2980	+	4.73958i	−7.37365	+	4.25718i
5.2	−1.38331	−	0.294032i	−3.10322	−	0.326162i	1.82709	+	0.813473i	−0.789828	+	0.711164i	4.19681	+	1.36363i	4.99632	+	4.90273i	−2.28825	−	1.66251i	0.720267	+	0.153097i	1.30168	−	0.751526i
5.3	−1.38331	−	0.294032i	−2.59406	−	0.272647i	1.82709	+	0.813473i	2.23534	−	2.01271i	3.50822	+	1.13989i	−5.59253	+	4.20994i	−2.28825	−	1.66251i	−2.14853	−	0.456683i	−3.68397	+	2.12694i
5.4	−1.38331	−	0.294032i	0.0286624	+	0.00301254i	1.82709	+	0.813473i	−3.53275	+	3.18090i	−0.0387632	−	0.0125949i	6.96364	−	0.712590i	−2.28825	−	1.66251i	−8.80252	−	1.87103i	5.82216	−	3.36143i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
11.c	even	5	1	inner
77.p	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.o.a	✓	128
7.d	odd	6	1	inner	154.3.o.a	✓	128
11.c	even	5	1	inner	154.3.o.a	✓	128
77.p	odd	30	1	inner	154.3.o.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
154.3.o.a	✓	128	1.a	even	1	1	trivial
154.3.o.a	✓	128	7.d	odd	6	1	inner
154.3.o.a	✓	128	11.c	even	5	1	inner
154.3.o.a	✓	128	77.p	odd	30	1	inner

Hecke kernels

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