Newform orbit 105.2.x.a

• Label: 105.2.x.a
• Level: $105$
• Weight: $2$
• Character orbit: 105.x
• Analytic conductor: $0.838$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.x (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.838429221223\)
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−0.631395	−	2.35640i	0.102851	−	1.72899i	−3.42191	+	1.97564i	−1.90893	+	1.16447i	−4.13914	+	0.849321i	1.82148	−	1.91891i	3.36596	+	3.36596i	−2.97884	−	0.355658i	3.94925	+	3.76295i
2.2	−0.582118	−	2.17249i	1.60750	+	0.644934i	−2.64881	+	1.52929i	2.21039	+	0.337883i	0.465359	−	3.86771i	−1.15099	−	2.38227i	1.68355	+	1.68355i	2.16812	+	2.07346i	−0.552660	−	4.99875i
2.3	−0.391246	−	1.46015i	−0.879005	−	1.49243i	−0.246919	+	0.142558i	1.82416	−	1.29322i	−1.83527	+	1.86739i	−1.17707	+	2.36949i	−1.83305	−	1.83305i	−1.45470	+	2.62371i	−2.60200	−	2.15759i
2.4	−0.340162	−	1.26950i	−0.664627	+	1.59946i	0.236127	−	0.136328i	1.25032	+	1.85383i	2.25660	+	0.299670i	2.32676	+	1.25943i	−2.11207	−	2.11207i	−2.11654	−	2.12609i	1.92813	−	2.21789i
2.5	−0.243110	−	0.907300i	−1.70312	+	0.315275i	0.967960	−	0.558852i	−1.66520	−	1.49235i	0.700094	+	1.46859i	0.0144144	−	2.64571i	−2.07075	−	2.07075i	2.80120	−	1.07390i	−0.949181	+	1.87364i
2.6	−0.0799329	−	0.298314i	1.29105	−	1.15464i	1.64945	−	0.952310i	−0.596180	+	2.15513i	−0.447643	−	0.292843i	−2.46856	+	0.951942i	−0.852694	−	0.852694i	0.333606	−	2.98139i	0.690558	+	0.00558322i
2.7	0.0799329	+	0.298314i	0.540759	+	1.64547i	1.64945	−	0.952310i	0.596180	−	2.15513i	−0.447643	+	0.292843i	−2.46856	+	0.951942i	0.852694	+	0.852694i	−2.41516	+	1.77961i	0.690558	+	0.00558322i
2.8	0.243110	+	0.907300i	−1.31730	−	1.12459i	0.967960	−	0.558852i	1.66520	+	1.49235i	0.700094	−	1.46859i	0.0144144	−	2.64571i	2.07075	+	2.07075i	0.470578	+	2.96286i	−0.949181	+	1.87364i
2.9	0.340162	+	1.26950i	0.224146	−	1.71749i	0.236127	−	0.136328i	−1.25032	−	1.85383i	2.25660	−	0.299670i	2.32676	+	1.25943i	2.11207	+	2.11207i	−2.89952	−	0.769934i	1.92813	−	2.21789i
2.10	0.391246	+	1.46015i	−1.50746	+	0.852980i	−0.246919	+	0.142558i	−1.82416	+	1.29322i	−1.83527	−	1.86739i	−1.17707	+	2.36949i	1.83305	+	1.83305i	1.54485	−	2.57166i	−2.60200	−	2.15759i
2.11	0.582118	+	2.17249i	1.71460	+	0.245221i	−2.64881	+	1.52929i	−2.21039	−	0.337883i	0.465359	+	3.86771i	−1.15099	−	2.38227i	−1.68355	−	1.68355i	2.87973	+	0.840915i	−0.552660	−	4.99875i
2.12	0.631395	+	2.35640i	−0.775426	+	1.54878i	−3.42191	+	1.97564i	1.90893	−	1.16447i	−4.13914	−	0.849321i	1.82148	−	1.91891i	−3.36596	−	3.36596i	−1.79743	−	2.40193i	3.94925	+	3.76295i
23.1	−2.35640	+	0.631395i	1.72899	+	0.102851i	3.42191	−	1.97564i	0.0540016	−	2.23542i	−4.13914	+	0.849321i	−1.91891	−	1.82148i	−3.36596	+	3.36596i	2.97884	+	0.355658i	1.28418	+	5.30163i
23.2	−2.17249	+	0.582118i	−0.644934	+	1.60750i	2.64881	−	1.52929i	1.39781	+	1.74531i	0.465359	−	3.86771i	−2.38227	+	1.15099i	−1.68355	+	1.68355i	−2.16812	−	2.07346i	−4.05271	−	2.97799i
23.3	−1.46015	+	0.391246i	1.49243	−	0.879005i	0.246919	−	0.142558i	−0.207883	+	2.22638i	−1.83527	+	1.86739i	2.36949	+	1.17707i	1.83305	−	1.83305i	1.45470	−	2.62371i	−0.567525	−	3.33219i
23.4	−1.26950	+	0.340162i	−1.59946	−	0.664627i	−0.236127	+	0.136328i	2.23063	+	0.155895i	2.25660	+	0.299670i	1.25943	−	2.32676i	2.11207	−	2.11207i	2.11654	+	2.12609i	−2.88481	+	0.560865i
23.5	−0.907300	+	0.243110i	−0.315275	−	1.70312i	−0.967960	+	0.558852i	−2.12501	−	0.695932i	0.700094	+	1.46859i	−2.64571	−	0.0144144i	2.07075	−	2.07075i	−2.80120	+	1.07390i	2.09721	+	0.114806i
23.6	−0.298314	+	0.0799329i	1.15464	+	1.29105i	−1.64945	+	0.952310i	1.56830	−	1.59387i	−0.447643	−	0.292843i	0.951942	+	2.46856i	0.852694	−	0.852694i	−0.333606	+	2.98139i	−0.340444	+	0.600832i
23.7	0.298314	−	0.0799329i	−1.64547	+	0.540759i	−1.64945	+	0.952310i	−1.56830	+	1.59387i	−0.447643	+	0.292843i	0.951942	+	2.46856i	−0.852694	+	0.852694i	2.41516	−	1.77961i	−0.340444	+	0.600832i
23.8	0.907300	−	0.243110i	1.12459	−	1.31730i	−0.967960	+	0.558852i	2.12501	+	0.695932i	0.700094	−	1.46859i	−2.64571	−	0.0144144i	−2.07075	+	2.07075i	−0.470578	−	2.96286i	2.09721	+	0.114806i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.c	even	3	1	inner
15.e	even	4	1	inner
21.h	odd	6	1	inner
35.l	odd	12	1	inner
105.x	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.2.x.a	✓	48
3.b	odd	2	1	inner	105.2.x.a	✓	48
5.b	even	2	1		525.2.bf.f		48
5.c	odd	4	1	inner	105.2.x.a	✓	48
5.c	odd	4	1		525.2.bf.f		48
7.b	odd	2	1		735.2.y.i		48
7.c	even	3	1	inner	105.2.x.a	✓	48
7.c	even	3	1		735.2.j.g		24
7.d	odd	6	1		735.2.j.e		24
7.d	odd	6	1		735.2.y.i		48
15.d	odd	2	1		525.2.bf.f		48
15.e	even	4	1	inner	105.2.x.a	✓	48
15.e	even	4	1		525.2.bf.f		48
21.c	even	2	1		735.2.y.i		48
21.g	even	6	1		735.2.j.e		24
21.g	even	6	1		735.2.y.i		48
21.h	odd	6	1	inner	105.2.x.a	✓	48
21.h	odd	6	1		735.2.j.g		24
35.f	even	4	1		735.2.y.i		48
35.j	even	6	1		525.2.bf.f		48
35.k	even	12	1		735.2.j.e		24
35.k	even	12	1		735.2.y.i		48
35.l	odd	12	1	inner	105.2.x.a	✓	48
35.l	odd	12	1		525.2.bf.f		48
35.l	odd	12	1		735.2.j.g		24
105.k	odd	4	1		735.2.y.i		48
105.o	odd	6	1		525.2.bf.f		48
105.w	odd	12	1		735.2.j.e		24
105.w	odd	12	1		735.2.y.i		48
105.x	even	12	1	inner	105.2.x.a	✓	48
105.x	even	12	1		525.2.bf.f		48
105.x	even	12	1		735.2.j.g		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.2.x.a	✓	48	1.a	even	1	1	trivial
105.2.x.a	✓	48	3.b	odd	2	1	inner
105.2.x.a	✓	48	5.c	odd	4	1	inner
105.2.x.a	✓	48	7.c	even	3	1	inner
105.2.x.a	✓	48	15.e	even	4	1	inner
105.2.x.a	✓	48	21.h	odd	6	1	inner
105.2.x.a	✓	48	35.l	odd	12	1	inner
105.2.x.a	✓	48	105.x	even	12	1	inner
525.2.bf.f		48	5.b	even	2	1
525.2.bf.f		48	5.c	odd	4	1
525.2.bf.f		48	15.d	odd	2	1
525.2.bf.f		48	15.e	even	4	1
525.2.bf.f		48	35.j	even	6	1
525.2.bf.f		48	35.l	odd	12	1
525.2.bf.f		48	105.o	odd	6	1
525.2.bf.f		48	105.x	even	12	1
735.2.j.e		24	7.d	odd	6	1
735.2.j.e		24	21.g	even	6	1
735.2.j.e		24	35.k	even	12	1
735.2.j.e		24	105.w	odd	12	1
735.2.j.g		24	7.c	even	3	1
735.2.j.g		24	21.h	odd	6	1
735.2.j.g		24	35.l	odd	12	1
735.2.j.g		24	105.x	even	12	1
735.2.y.i		48	7.b	odd	2	1
735.2.y.i		48	7.d	odd	6	1
735.2.y.i		48	21.c	even	2	1
735.2.y.i		48	21.g	even	6	1
735.2.y.i		48	35.f	even	4	1
735.2.y.i		48	35.k	even	12	1
735.2.y.i		48	105.k	odd	4	1
735.2.y.i		48	105.w	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(105, [\chi])\).