Newform orbit 245.4.j.g

• Label: 245.4.j.g
• Level: $245$
• Weight: $4$
• Character orbit: 245.j
• Analytic conductor: $14.455$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.4554679514\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 44 q^{4} - 140 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
79.1	−4.20246	−	2.42629i	−0.991781	+	0.572605i	7.77380	+	13.4646i	−4.34186	+	10.3028i	5.55723				0			−	36.6254i	−12.8442	+	22.2469i	43.2442	−	32.7626i
79.2	−4.20246	−	2.42629i	0.991781	−	0.572605i	7.77380	+	13.4646i	4.34186	−	10.3028i	−5.55723				0			−	36.6254i	−12.8442	+	22.2469i	−43.2442	+	32.7626i
79.3	−2.82920	−	1.63344i	−4.95822	+	2.86263i	1.33624	+	2.31444i	4.95482	−	10.0225i	18.7037				0				17.4043i	2.88927	−	5.00437i	−30.3892	+	20.2621i
79.4	−2.82920	−	1.63344i	4.95822	−	2.86263i	1.33624	+	2.31444i	−4.95482	+	10.0225i	−18.7037				0				17.4043i	2.88927	−	5.00437i	30.3892	−	20.2621i
79.5	−0.764808	−	0.441562i	−2.98872	+	1.72554i	−3.61005	−	6.25278i	10.9666	+	2.17557i	3.04773				0				13.4412i	−7.54503	+	13.0684i	−7.42671	−	6.50634i
79.6	−0.764808	−	0.441562i	2.98872	−	1.72554i	−3.61005	−	6.25278i	−10.9666	−	2.17557i	−3.04773				0				13.4412i	−7.54503	+	13.0684i	7.42671	+	6.50634i
79.7	0.764808	+	0.441562i	−2.98872	+	1.72554i	−3.61005	−	6.25278i	7.36741	+	8.40959i	−3.04773				0			−	13.4412i	−7.54503	+	13.0684i	1.92130	+	9.68490i
79.8	0.764808	+	0.441562i	2.98872	−	1.72554i	−3.61005	−	6.25278i	−7.36741	−	8.40959i	3.04773				0			−	13.4412i	−7.54503	+	13.0684i	−1.92130	−	9.68490i
79.9	2.82920	+	1.63344i	−4.95822	+	2.86263i	1.33624	+	2.31444i	−6.20230	+	9.30223i	−18.7037				0			−	17.4043i	2.88927	−	5.00437i	−32.7422	+	16.1868i
79.10	2.82920	+	1.63344i	4.95822	−	2.86263i	1.33624	+	2.31444i	6.20230	−	9.30223i	18.7037				0			−	17.4043i	2.88927	−	5.00437i	32.7422	−	16.1868i
79.11	4.20246	+	2.42629i	−0.991781	+	0.572605i	7.77380	+	13.4646i	6.75158	−	8.91157i	−5.55723				0				36.6254i	−12.8442	+	22.2469i	49.9954	−	21.0693i
79.12	4.20246	+	2.42629i	0.991781	−	0.572605i	7.77380	+	13.4646i	−6.75158	+	8.91157i	5.55723				0				36.6254i	−12.8442	+	22.2469i	−49.9954	+	21.0693i
214.1	−4.20246	+	2.42629i	−0.991781	−	0.572605i	7.77380	−	13.4646i	−4.34186	−	10.3028i	5.55723				0				36.6254i	−12.8442	−	22.2469i	43.2442	+	32.7626i
214.2	−4.20246	+	2.42629i	0.991781	+	0.572605i	7.77380	−	13.4646i	4.34186	+	10.3028i	−5.55723				0				36.6254i	−12.8442	−	22.2469i	−43.2442	−	32.7626i
214.3	−2.82920	+	1.63344i	−4.95822	−	2.86263i	1.33624	−	2.31444i	4.95482	+	10.0225i	18.7037				0			−	17.4043i	2.88927	+	5.00437i	−30.3892	−	20.2621i
214.4	−2.82920	+	1.63344i	4.95822	+	2.86263i	1.33624	−	2.31444i	−4.95482	−	10.0225i	−18.7037				0			−	17.4043i	2.88927	+	5.00437i	30.3892	+	20.2621i
214.5	−0.764808	+	0.441562i	−2.98872	−	1.72554i	−3.61005	+	6.25278i	10.9666	−	2.17557i	3.04773				0			−	13.4412i	−7.54503	−	13.0684i	−7.42671	+	6.50634i
214.6	−0.764808	+	0.441562i	2.98872	+	1.72554i	−3.61005	+	6.25278i	−10.9666	+	2.17557i	−3.04773				0			−	13.4412i	−7.54503	−	13.0684i	7.42671	−	6.50634i
214.7	0.764808	−	0.441562i	−2.98872	−	1.72554i	−3.61005	+	6.25278i	7.36741	−	8.40959i	−3.04773				0				13.4412i	−7.54503	−	13.0684i	1.92130	−	9.68490i
214.8	0.764808	−	0.441562i	2.98872	+	1.72554i	−3.61005	+	6.25278i	−7.36741	+	8.40959i	3.04773				0				13.4412i	−7.54503	−	13.0684i	−1.92130	+	9.68490i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.b	odd	2	1	inner
7.c	even	3	1	inner
7.d	odd	6	1	inner
35.c	odd	2	1	inner
35.i	odd	6	1	inner
35.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	245.4.j.g		24
5.b	even	2	1	inner	245.4.j.g		24
7.b	odd	2	1	inner	245.4.j.g		24
7.c	even	3	1		245.4.b.g	✓	12
7.c	even	3	1	inner	245.4.j.g		24
7.d	odd	6	1		245.4.b.g	✓	12
7.d	odd	6	1	inner	245.4.j.g		24
35.c	odd	2	1	inner	245.4.j.g		24
35.i	odd	6	1		245.4.b.g	✓	12
35.i	odd	6	1	inner	245.4.j.g		24
35.j	even	6	1		245.4.b.g	✓	12
35.j	even	6	1	inner	245.4.j.g		24
35.k	even	12	2		1225.4.a.bs		12
35.l	odd	12	2		1225.4.a.bs		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
245.4.b.g	✓	12	7.c	even	3	1
245.4.b.g	✓	12	7.d	odd	6	1
245.4.b.g	✓	12	35.i	odd	6	1
245.4.b.g	✓	12	35.j	even	6	1
245.4.j.g		24	1.a	even	1	1	trivial
245.4.j.g		24	5.b	even	2	1	inner
245.4.j.g		24	7.b	odd	2	1	inner
245.4.j.g		24	7.c	even	3	1	inner
245.4.j.g		24	7.d	odd	6	1	inner
245.4.j.g		24	35.c	odd	2	1	inner
245.4.j.g		24	35.i	odd	6	1	inner
245.4.j.g		24	35.j	even	6	1	inner
1225.4.a.bs		12	35.k	even	12	2
1225.4.a.bs		12	35.l	odd	12	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(245, [\chi])\):

\( T_{2}^{12} - 35T_{2}^{10} + 947T_{2}^{8} - 9338T_{2}^{6} + 70424T_{2}^{4} - 54488T_{2}^{2} + 38416 \)

T19^12 + 19440*T19^10 + 376913088*T19^8 + 19440118784*T19^6 + 905432961024*T19^4 + 4919765630976*T19^2 + 24179327893504