Newform orbit 108.5.f.a

• Label: 108.5.f.a
• Level: $108$
• Weight: $5$
• Character orbit: 108.f
• Analytic conductor: $11.164$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.1639560131\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 36)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−3.99035	−	0.277636i		0		15.8458	+	2.21573i	23.3466	+	40.4374i		0		52.4363	+	30.2741i	−62.6153	−	13.2409i		0		−81.9341	−	167.841i
19.2	−3.89672	−	0.903087i		0		14.3689	+	7.03816i	−19.5394	−	33.8433i		0		10.5700	+	6.10260i	−49.6354	−	40.4021i		0		45.5763	+	149.524i
19.3	−3.68138	+	1.56444i		0		11.1051	−	11.5186i	−1.01545	−	1.75881i		0		20.0352	+	11.5673i	−22.8618	+	59.7774i		0		6.48981	+	4.88624i
19.4	−3.61656	−	1.70894i		0		10.1591	+	12.3610i	2.83091	+	4.90328i		0		−45.1595	−	26.0728i	−15.6169	−	62.0654i		0		−1.85878	−	22.5709i
19.5	−3.42968	+	2.05847i		0		7.52540	−	14.1198i	−16.6139	−	28.7760i		0		−39.9759	−	23.0801i	3.25547	+	63.9171i		0		116.215	+	64.4935i
19.6	−2.63137	+	3.01262i		0		−2.15179	−	15.8546i	10.5756	+	18.3175i		0		−38.6407	−	22.3092i	53.4262	+	35.2369i		0		−83.0119	−	16.3397i
19.7	−2.58866	−	3.04940i		0		−2.59770	+	15.7877i	5.51579	+	9.55363i		0		10.3188	+	5.95759i	54.8676	−	32.9476i		0		14.8544	−	41.5509i
19.8	−1.52726	−	3.69695i		0		−11.3349	+	11.2924i	−11.0746	−	19.1817i		0		82.7885	+	47.7980i	59.0591	+	24.6582i		0		−54.0000	+	70.2376i
19.9	−1.29332	+	3.78514i		0		−12.6546	−	9.79083i	10.5756	+	18.3175i		0		38.6407	+	22.3092i	53.4262	−	35.2369i		0		−83.0119	+	16.3397i
19.10	−1.04046	−	3.86231i		0		−13.8349	+	8.03717i	5.89438	+	10.2094i		0		−50.5548	−	29.1878i	45.4367	+	45.0722i		0		33.2988	−	33.3884i
19.11	−0.0678484	+	3.99942i		0		−15.9908	−	0.542709i	−16.6139	−	28.7760i		0		39.9759	+	23.0801i	3.25547	−	63.9171i		0		116.215	−	64.4935i
19.12	0.485844	+	3.97038i		0		−15.5279	+	3.85798i	−1.01545	−	1.75881i		0		−20.0352	−	11.5673i	−22.8618	−	59.7774i		0		6.48981	−	4.88624i
19.13	0.701741	−	3.93796i		0		−15.0151	−	5.52686i	−14.3046	−	24.7763i		0		−22.2124	−	12.8243i	−32.3013	+	55.2506i		0		−107.606	+	38.9445i
19.14	1.85603	−	3.54333i		0		−9.11034	−	13.1530i	14.8847	+	25.7811i		0		−51.8739	−	29.9494i	−63.5145	+	7.86857i		0		118.977	−	4.89106i
19.15	2.14060	−	3.37903i		0		−6.83568	−	14.4663i	14.8847	+	25.7811i		0		51.8739	+	29.9494i	−63.5145	−	7.86857i		0		118.977	+	4.89106i
19.16	2.23562	+	3.31693i		0		−6.00404	+	14.8308i	23.3466	+	40.4374i		0		−52.4363	−	30.2741i	−62.6153	+	13.2409i		0		−81.9341	+	167.841i
19.17	2.73046	+	2.92312i		0		−1.08921	+	15.9629i	−19.5394	−	33.8433i		0		−10.5700	−	6.10260i	−49.6354	+	40.4021i		0		45.5763	−	149.524i
19.18	3.05951	−	2.57671i		0		2.72116	−	15.7669i	−14.3046	−	24.7763i		0		22.2124	+	12.8243i	−32.3013	−	55.2506i		0		−107.606	−	38.9445i
19.19	3.28826	+	2.27757i		0		5.62536	+	14.9785i	2.83091	+	4.90328i		0		45.1595	+	26.0728i	−15.6169	+	62.0654i		0		−1.85878	+	22.5709i
19.20	3.86509	−	1.03009i		0		13.8778	−	7.96277i	5.89438	+	10.2094i		0		50.5548	+	29.1878i	45.4367	−	45.0722i		0		33.2988	+	33.3884i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
9.c	even	3	1	inner
36.f	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	108.5.f.a		44
3.b	odd	2	1		36.5.f.a	✓	44
4.b	odd	2	1	inner	108.5.f.a		44
9.c	even	3	1	inner	108.5.f.a		44
9.c	even	3	1		324.5.d.e		22
9.d	odd	6	1		36.5.f.a	✓	44
9.d	odd	6	1		324.5.d.f		22
12.b	even	2	1		36.5.f.a	✓	44
36.f	odd	6	1	inner	108.5.f.a		44
36.f	odd	6	1		324.5.d.e		22
36.h	even	6	1		36.5.f.a	✓	44
36.h	even	6	1		324.5.d.f		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
36.5.f.a	✓	44	3.b	odd	2	1
36.5.f.a	✓	44	9.d	odd	6	1
36.5.f.a	✓	44	12.b	even	2	1
36.5.f.a	✓	44	36.h	even	6	1
108.5.f.a		44	1.a	even	1	1	trivial
108.5.f.a		44	4.b	odd	2	1	inner
108.5.f.a		44	9.c	even	3	1	inner
108.5.f.a		44	36.f	odd	6	1	inner
324.5.d.e		22	9.c	even	3	1
324.5.d.e		22	36.f	odd	6	1
324.5.d.f		22	9.d	odd	6	1
324.5.d.f		22	36.h	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(108, [\chi])\).