Newform orbit 104.2.u.a

• Label: 104.2.u.a
• Level: $104$
• Weight: $2$
• Character orbit: 104.u
• Analytic conductor: $0.830$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.u (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.830444181021\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{2} - 4 q^{3} - 6 q^{4} - 6 q^{6} - 10 q^{8} - 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.35755	+	0.396300i	−1.57612	−	2.72991i	1.68589	−	1.07599i	−2.13831	+	2.13831i	3.22152	+	3.08138i	−1.43298	+	0.383965i	−1.86227	+	2.12884i	−3.46828	+	6.00723i	2.05545	−	3.75028i
11.2	−1.28449	−	0.591686i	−0.223033	−	0.386304i	1.29981	+	1.52003i	0.612771	−	0.612771i	0.0579118	+	0.628168i	2.00697	−	0.537767i	−0.770215	−	2.72154i	1.40051	−	2.42576i	−1.14967	+	0.424528i
11.3	−1.22577	+	0.705331i	0.0597334	+	0.103461i	1.00502	−	1.72914i	2.08890	−	2.08890i	−0.146194	−	0.0846877i	−1.83497	+	0.491678i	−0.0122979	+	2.82840i	1.49286	−	2.58572i	−1.08714	+	4.03388i
11.4	−0.899259	+	1.09148i	1.05427	+	1.82605i	−0.382666	−	1.96305i	−2.29020	+	2.29020i	−2.94117	−	0.491377i	1.21025	−	0.324286i	2.48675	+	1.34762i	−0.722984	+	1.25224i	−0.440228	−	4.55919i
11.5	−0.376293	−	1.36323i	1.11333	+	1.92835i	−1.71681	+	1.02595i	0.0693382	−	0.0693382i	2.20985	−	2.24336i	3.36551	−	0.901786i	2.04463	+	1.95435i	−0.979029	+	1.69573i	−0.120616	−	0.0684326i
11.6	−0.195127	−	1.40069i	−0.928193	−	1.60768i	−1.92385	+	0.546624i	1.51817	−	1.51817i	−2.07074	+	1.61381i	−2.97768	+	0.797866i	1.14104	+	2.58805i	−0.223086	+	0.386396i	−2.42271	−	1.83024i
11.7	0.233040	+	1.39488i	1.05427	+	1.82605i	−1.89138	+	0.650127i	2.29020	−	2.29020i	−2.30144	+	1.89613i	−1.21025	+	0.324286i	−1.34762	−	2.48675i	−0.722984	+	1.25224i	3.72826	+	2.66085i
11.8	0.708881	+	1.22372i	0.0597334	+	0.103461i	−0.994975	+	1.73494i	−2.08890	+	2.08890i	−0.0842636	+	0.146439i	1.83497	−	0.491678i	−2.82840	+	0.0122979i	1.49286	−	2.58572i	−4.03702	−	1.07545i
11.9	0.869329	−	1.11547i	−0.928193	−	1.60768i	−0.488535	−	1.93942i	−1.51817	+	1.51817i	−2.60022	−	0.362231i	2.97768	−	0.797866i	−2.58805	−	1.14104i	−0.223086	+	0.386396i	0.373680	+	3.01325i
11.10	0.977524	+	1.02198i	−1.57612	−	2.72991i	−0.0888919	+	1.99802i	2.13831	−	2.13831i	1.24923	−	4.27932i	1.43298	−	0.383965i	−2.12884	+	1.86227i	−3.46828	+	6.00723i	4.27556	+	0.0950627i
11.11	1.00750	−	0.992447i	1.11333	+	1.92835i	0.0300962	−	1.99977i	−0.0693382	+	0.0693382i	3.03547	+	0.837881i	−3.36551	+	0.901786i	−1.95435	−	2.04463i	−0.979029	+	1.69573i	−0.00104344	+	0.138673i
11.12	1.40824	+	0.129828i	−0.223033	−	0.386304i	1.96629	+	0.365659i	−0.612771	+	0.612771i	−0.263931	−	0.572966i	−2.00697	+	0.537767i	2.72154	+	0.770215i	1.40051	−	2.42576i	−0.942485	+	0.783375i
19.1	−1.35755	−	0.396300i	−1.57612	+	2.72991i	1.68589	+	1.07599i	−2.13831	−	2.13831i	3.22152	−	3.08138i	−1.43298	−	0.383965i	−1.86227	−	2.12884i	−3.46828	−	6.00723i	2.05545	+	3.75028i
19.2	−1.28449	+	0.591686i	−0.223033	+	0.386304i	1.29981	−	1.52003i	0.612771	+	0.612771i	0.0579118	−	0.628168i	2.00697	+	0.537767i	−0.770215	+	2.72154i	1.40051	+	2.42576i	−1.14967	−	0.424528i
19.3	−1.22577	−	0.705331i	0.0597334	−	0.103461i	1.00502	+	1.72914i	2.08890	+	2.08890i	−0.146194	+	0.0846877i	−1.83497	−	0.491678i	−0.0122979	−	2.82840i	1.49286	+	2.58572i	−1.08714	−	4.03388i
19.4	−0.899259	−	1.09148i	1.05427	−	1.82605i	−0.382666	+	1.96305i	−2.29020	−	2.29020i	−2.94117	+	0.491377i	1.21025	+	0.324286i	2.48675	−	1.34762i	−0.722984	−	1.25224i	−0.440228	+	4.55919i
19.5	−0.376293	+	1.36323i	1.11333	−	1.92835i	−1.71681	−	1.02595i	0.0693382	+	0.0693382i	2.20985	+	2.24336i	3.36551	+	0.901786i	2.04463	−	1.95435i	−0.979029	−	1.69573i	−0.120616	+	0.0684326i
19.6	−0.195127	+	1.40069i	−0.928193	+	1.60768i	−1.92385	−	0.546624i	1.51817	+	1.51817i	−2.07074	−	1.61381i	−2.97768	−	0.797866i	1.14104	−	2.58805i	−0.223086	−	0.386396i	−2.42271	+	1.83024i
19.7	0.233040	−	1.39488i	1.05427	−	1.82605i	−1.89138	−	0.650127i	2.29020	+	2.29020i	−2.30144	−	1.89613i	−1.21025	−	0.324286i	−1.34762	+	2.48675i	−0.722984	−	1.25224i	3.72826	−	2.66085i
19.8	0.708881	−	1.22372i	0.0597334	−	0.103461i	−0.994975	−	1.73494i	−2.08890	−	2.08890i	−0.0842636	−	0.146439i	1.83497	+	0.491678i	−2.82840	−	0.0122979i	1.49286	+	2.58572i	−4.03702	+	1.07545i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
13.f	odd	12	1	inner
104.u	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	104.2.u.a	✓	48
3.b	odd	2	1		936.2.ed.d		48
4.b	odd	2	1		416.2.bk.a		48
8.b	even	2	1		416.2.bk.a		48
8.d	odd	2	1	inner	104.2.u.a	✓	48
13.f	odd	12	1	inner	104.2.u.a	✓	48
24.f	even	2	1		936.2.ed.d		48
39.k	even	12	1		936.2.ed.d		48
52.l	even	12	1		416.2.bk.a		48
104.u	even	12	1	inner	104.2.u.a	✓	48
104.x	odd	12	1		416.2.bk.a		48
312.bq	odd	12	1		936.2.ed.d		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
104.2.u.a	✓	48	1.a	even	1	1	trivial
104.2.u.a	✓	48	8.d	odd	2	1	inner
104.2.u.a	✓	48	13.f	odd	12	1	inner
104.2.u.a	✓	48	104.u	even	12	1	inner
416.2.bk.a		48	4.b	odd	2	1
416.2.bk.a		48	8.b	even	2	1
416.2.bk.a		48	52.l	even	12	1
416.2.bk.a		48	104.x	odd	12	1
936.2.ed.d		48	3.b	odd	2	1
936.2.ed.d		48	24.f	even	2	1
936.2.ed.d		48	39.k	even	12	1
936.2.ed.d		48	312.bq	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(104, [\chi])\).