Newform orbit 123.3.k.a

• Label: 123.3.k.a
• Level: $123$
• Weight: $3$
• Character orbit: 123.k
• Analytic conductor: $3.352$
• Analytic rank: $0$
• Dimension: $104$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	123.k (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.35150725163\)
Analytic rank:	\(0\)
Dimension:	\(104\)
Relative dimension:	\(26\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 104 q - 12 q^{3} + 42 q^{4} - 5 q^{6} - 6 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
59.1	−3.59174	+	1.16703i	−0.907092	+	2.85958i	8.30258	−	6.03218i	−0.725592	−	0.998692i	−0.0791666	−	11.3295i	−4.20511	+	12.9420i	−13.9017	+	19.1341i	−7.35437	−	5.18780i	3.77164	+	2.74026i
59.2	−3.48875	+	1.13356i	0.624459	−	2.93429i	7.65033	−	5.55829i	2.46428	+	3.39180i	1.14762	+	10.9449i	0.337466	−	1.03861i	−11.7647	+	16.1928i	−8.22010	−	3.66469i	−12.4421	−	9.03970i
59.3	−3.03305	+	0.985498i	−2.94512	+	0.571205i	4.99212	−	3.62699i	2.70671	+	3.72547i	8.36977	−	4.63490i	2.87922	−	8.86133i	−4.06884	+	5.60028i	8.34745	−	3.36453i	−11.8810	−	8.63209i
59.4	−2.99646	+	0.973609i	−2.34524	−	1.87079i	4.79480	−	3.48362i	−4.93648	−	6.79449i	8.84884	+	3.32240i	0.0470146	−	0.144696i	−3.56807	+	4.91103i	2.00031	+	8.77489i	21.4072	+	15.5532i
59.5	−2.64704	+	0.860075i	2.84366	+	0.955812i	3.03102	−	2.20217i	2.29791	+	3.16280i	−8.34936	−	0.0843074i	−1.12160	+	3.45193i	0.414637	−	0.570699i	7.17285	+	5.43602i	−8.80291	−	6.39569i
59.6	−2.47108	+	0.802901i	0.838332	+	2.88049i	2.22550	−	1.61692i	−3.08615	−	4.24772i	−4.38433	−	6.44480i	2.86544	−	8.81890i	1.90768	−	2.62570i	−7.59440	+	4.82961i	11.0366	+	8.01857i
59.7	−2.23248	+	0.725378i	2.25801	−	1.97519i	1.22174	−	0.887646i	−1.05563	−	1.45294i	−3.60822	+	6.04749i	0.469748	−	1.44574i	3.43537	−	4.72838i	1.19726	−	8.92001i	3.41060	+	2.47795i
59.8	−1.37260	+	0.445985i	−0.795179	+	2.89270i	−1.55094	+	1.12682i	4.55947	+	6.27557i	−0.198636	−	4.32516i	−0.395355	+	1.21678i	5.01953	−	6.90879i	−7.73538	−	4.60042i	−9.05714	−	6.58040i
59.9	−1.34285	+	0.436317i	−0.337088	−	2.98100i	−1.62321	+	1.17933i	−0.313022	−	0.430838i	1.75332	+	3.85595i	−1.41150	+	4.34414i	4.98485	−	6.86106i	−8.77274	+	2.00972i	0.608322	+	0.441972i
59.10	−1.19967	+	0.389798i	−2.85969	+	0.906741i	−1.94879	+	1.41588i	−1.66079	−	2.28587i	3.07725	−	2.20250i	−1.38422	+	4.26018i	4.75177	−	6.54025i	7.35564	−	5.18600i	2.88343	+	2.09493i
59.11	−0.740169	+	0.240495i	−1.81206	−	2.39091i	−2.74606	+	1.99513i	3.50478	+	4.82391i	1.91623	+	1.33388i	3.13242	−	9.64059i	3.38252	−	4.65564i	−2.43289	+	8.66493i	−3.75426	−	2.72763i
59.12	−0.404054	+	0.131285i	2.32952	+	1.89033i	−3.09004	+	2.24505i	−4.83021	−	6.64821i	−1.18942	−	0.457965i	−4.03348	+	12.4138i	1.95268	−	2.68763i	1.85329	+	8.80712i	2.82448	+	2.05210i
59.13	−0.307199	+	0.0998149i	2.72551	−	1.25362i	−3.15166	+	2.28981i	−2.93357	−	4.03771i	−0.712144	+	0.657159i	2.62897	−	8.09113i	1.49907	−	2.06329i	5.85685	−	6.83354i	1.30421	+	0.947565i
59.14	0.307199	−	0.0998149i	2.72551	+	1.25362i	−3.15166	+	2.28981i	2.93357	+	4.03771i	0.962405	+	0.113065i	2.62897	−	8.09113i	−1.49907	+	2.06329i	5.85685	+	6.83354i	1.30421	+	0.947565i
59.15	0.404054	−	0.131285i	2.32952	−	1.89033i	−3.09004	+	2.24505i	4.83021	+	6.64821i	0.693078	−	1.06963i	−4.03348	+	12.4138i	−1.95268	+	2.68763i	1.85329	−	8.80712i	2.82448	+	2.05210i
59.16	0.740169	−	0.240495i	−1.81206	+	2.39091i	−2.74606	+	1.99513i	−3.50478	−	4.82391i	−0.766226	+	2.20547i	3.13242	−	9.64059i	−3.38252	+	4.65564i	−2.43289	−	8.66493i	−3.75426	−	2.72763i
59.17	1.19967	−	0.389798i	−2.85969	−	0.906741i	−1.94879	+	1.41588i	1.66079	+	2.28587i	−3.78414	+	0.0269060i	−1.38422	+	4.26018i	−4.75177	+	6.54025i	7.35564	+	5.18600i	2.88343	+	2.09493i
59.18	1.34285	−	0.436317i	−0.337088	+	2.98100i	−1.62321	+	1.17933i	0.313022	+	0.430838i	0.848004	+	4.15010i	−1.41150	+	4.34414i	−4.98485	+	6.86106i	−8.77274	−	2.00972i	0.608322	+	0.441972i
59.19	1.37260	−	0.445985i	−0.795179	−	2.89270i	−1.55094	+	1.12682i	−4.55947	−	6.27557i	−2.38156	−	3.61588i	−0.395355	+	1.21678i	−5.01953	+	6.90879i	−7.73538	+	4.60042i	−9.05714	−	6.58040i
59.20	2.23248	−	0.725378i	2.25801	+	1.97519i	1.22174	−	0.887646i	1.05563	+	1.45294i	6.47374	+	2.77166i	0.469748	−	1.44574i	−3.43537	+	4.72838i	1.19726	+	8.92001i	3.41060	+	2.47795i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
41.d	even	5	1	inner
123.k	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	123.3.k.a	✓	104
3.b	odd	2	1	inner	123.3.k.a	✓	104
41.d	even	5	1	inner	123.3.k.a	✓	104
123.k	odd	10	1	inner	123.3.k.a	✓	104

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
123.3.k.a	✓	104	1.a	even	1	1	trivial
123.3.k.a	✓	104	3.b	odd	2	1	inner
123.3.k.a	✓	104	41.d	even	5	1	inner
123.3.k.a	✓	104	123.k	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(123, [\chi])\).