Newform orbit 124.5.i.a

• Label: 124.5.i.a
• Level: $124$
• Weight: $5$
• Character orbit: 124.i
• Analytic conductor: $12.818$
• Analytic rank: $0$
• Dimension: $124$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.8178754224\)
Analytic rank:	\(0\)
Dimension:	\(124\)
Relative dimension:	\(62\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 124 q - 4 q^{2} - 32 q^{4} - 2 q^{5} + 212 q^{8} + 1564 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	−3.99851	−	0.109072i	4.29354	+	2.47888i	15.9762	+	0.872250i	12.1810	+	21.0980i	−16.8974	−	10.3801i	−61.1133	−	35.2838i	−63.7859	−	5.23026i	−28.2103	−	48.8617i	−46.4045	−	85.6893i
67.2	−3.99851	+	0.109072i	−4.29354	−	2.47888i	15.9762	−	0.872250i	12.1810	+	21.0980i	17.4382	+	9.44352i	61.1133	+	35.2838i	−63.7859	+	5.23026i	−28.2103	−	48.8617i	−51.0069	−	83.0321i
67.3	−3.96104	−	0.556897i	−13.1743	−	7.60620i	15.3797	+	4.41179i	−9.10408	−	15.7687i	47.9482	+	37.4653i	16.7158	+	9.65089i	−58.4629	−	26.0402i	75.2087	+	130.265i	27.2801	+	67.5307i
67.4	−3.96104	+	0.556897i	13.1743	+	7.60620i	15.3797	−	4.41179i	−9.10408	−	15.7687i	−56.4200	−	22.7918i	−16.7158	−	9.65089i	−58.4629	+	26.0402i	75.2087	+	130.265i	44.8432	+	57.3906i
67.5	−3.82637	−	1.16570i	4.04124	+	2.33321i	13.2823	+	8.92080i	−15.1375	−	26.2189i	−12.7435	−	13.6386i	48.4396	+	27.9666i	−40.4241	−	49.6175i	−29.6122	−	51.2899i	27.3583	+	117.969i
67.6	−3.82637	+	1.16570i	−4.04124	−	2.33321i	13.2823	−	8.92080i	−15.1375	−	26.2189i	18.1831	+	4.21687i	−48.4396	−	27.9666i	−40.4241	+	49.6175i	−29.6122	−	51.2899i	88.4850	+	82.6775i
67.7	−3.65497	−	1.62518i	14.0734	+	8.12529i	10.7176	+	11.8800i	8.08713	+	14.0073i	−38.2328	−	52.5695i	35.9919	+	20.7799i	−19.8652	−	60.8389i	91.5405	+	158.553i	−6.79373	−	64.3393i
67.8	−3.65497	+	1.62518i	−14.0734	−	8.12529i	10.7176	−	11.8800i	8.08713	+	14.0073i	64.6429	+	6.82578i	−35.9919	−	20.7799i	−19.8652	+	60.8389i	91.5405	+	158.553i	−52.3226	−	38.0532i
67.9	−3.57848	−	1.78731i	−8.22563	−	4.74907i	9.61106	+	12.7917i	−10.5069	−	18.1984i	20.9472	+	31.6962i	−30.8214	−	17.7948i	−11.5303	−	62.9528i	4.60732	+	7.98011i	5.07244	+	83.9018i
67.10	−3.57848	+	1.78731i	8.22563	+	4.74907i	9.61106	−	12.7917i	−10.5069	−	18.1984i	−37.9233	−	2.29273i	30.8214	+	17.7948i	−11.5303	+	62.9528i	4.60732	+	7.98011i	70.1249	+	46.3438i
67.11	−3.33266	−	2.21210i	−10.5786	−	6.10757i	6.21325	+	14.7443i	21.6007	+	37.4135i	21.7444	+	43.7554i	−21.7292	−	12.5454i	11.9093	−	62.8822i	34.1049	+	59.0714i	10.7745	−	172.469i
67.12	−3.33266	+	2.21210i	10.5786	+	6.10757i	6.21325	−	14.7443i	21.6007	+	37.4135i	−48.7655	+	3.04649i	21.7292	+	12.5454i	11.9093	+	62.8822i	34.1049	+	59.0714i	−154.750	−	76.9036i
67.13	−3.28486	−	2.28248i	3.74080	+	2.15975i	5.58060	+	14.9952i	3.50661	+	6.07364i	−7.35842	−	15.6328i	−20.7012	−	11.9518i	15.8948	−	61.9948i	−31.1709	−	53.9896i	2.34420	−	27.9548i
67.14	−3.28486	+	2.28248i	−3.74080	−	2.15975i	5.58060	−	14.9952i	3.50661	+	6.07364i	17.2176	−	1.44381i	20.7012	+	11.9518i	15.8948	+	61.9948i	−31.1709	−	53.9896i	−25.3817	−	11.9473i
67.15	−2.54741	−	3.08394i	12.2602	+	7.07841i	−3.02140	+	15.7121i	−8.80527	−	15.2512i	−9.40226	−	55.8412i	−57.7873	−	33.3635i	56.1521	−	30.7074i	59.7077	+	103.417i	−24.6031	+	66.0060i
67.16	−2.54741	+	3.08394i	−12.2602	−	7.07841i	−3.02140	−	15.7121i	−8.80527	−	15.2512i	53.0611	−	19.7780i	57.7873	+	33.3635i	56.1521	+	30.7074i	59.7077	+	103.417i	69.4644	+	11.6961i
67.17	−2.49213	−	3.12878i	6.05257	+	3.49445i	−3.57854	+	15.5947i	18.8621	+	32.6701i	−4.15044	−	27.6458i	45.3324	+	26.1727i	57.7105	−	27.6676i	−16.0776	−	27.8472i	55.2108	−	140.434i
67.18	−2.49213	+	3.12878i	−6.05257	−	3.49445i	−3.57854	−	15.5947i	18.8621	+	32.6701i	26.0172	−	10.2285i	−45.3324	−	26.1727i	57.7105	+	27.6676i	−16.0776	−	27.8472i	−149.225	−	22.4029i
67.19	−2.29228	−	3.27802i	−7.66968	−	4.42809i	−5.49089	+	15.0283i	4.34301	+	7.52232i	3.06567	+	35.2918i	32.6813	+	18.8685i	61.8498	−	16.4498i	−1.28398	−	2.22391i	14.7029	−	31.4798i
67.20	−2.29228	+	3.27802i	7.66968	+	4.42809i	−5.49089	−	15.0283i	4.34301	+	7.52232i	−32.0965	+	14.9910i	−32.6813	−	18.8685i	61.8498	+	16.4498i	−1.28398	−	2.22391i	−34.6138	−	3.00677i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.c	even	3	1	inner
124.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.5.i.a	✓	124
4.b	odd	2	1	inner	124.5.i.a	✓	124
31.c	even	3	1	inner	124.5.i.a	✓	124
124.i	odd	6	1	inner	124.5.i.a	✓	124

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.5.i.a	✓	124	1.a	even	1	1	trivial
124.5.i.a	✓	124	4.b	odd	2	1	inner
124.5.i.a	✓	124	31.c	even	3	1	inner
124.5.i.a	✓	124	124.i	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).