Newform orbit 108.4.l.a

• Label: 108.4.l.a
• Level: $108$
• Weight: $4$
• Character orbit: 108.l
• Analytic conductor: $6.372$
• Analytic rank: $0$
• Dimension: $312$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.37220628062\)
Analytic rank:	\(0\)
Dimension:	\(312\)
Relative dimension:	\(52\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 312 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \)

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	−2.82000	+	0.218140i	−2.56535	+	4.51874i	7.90483	−	1.23031i	2.35563	−	6.47204i	6.24857	−	13.3025i	−6.19890	−	1.09303i	−22.0233	+	5.19383i	−13.8380	−	23.1843i	−5.23107	+	18.7650i
11.2	−2.81863	+	0.235239i	−0.238051	−	5.19070i	7.88933	−	1.32610i	5.65263	−	15.5305i	1.89203	+	14.5746i	28.8083	+	5.07968i	−21.9251	+	5.59366i	−26.8867	+	2.47130i	−12.2793	+	45.1044i
11.3	−2.76593	+	0.591311i	−5.08011	+	1.09199i	7.30070	−	3.27105i	−6.87889	+	18.8996i	13.4055	−	6.02429i	22.1047	+	3.89766i	−18.2590	+	13.3645i	24.6151	−	11.0949i	7.85096	−	56.3424i
11.4	−2.75026	−	0.660376i	2.16188	−	4.72507i	7.12781	+	3.63240i	−3.60998	+	9.91833i	−9.06605	+	11.5675i	−12.1874	−	2.14897i	−17.2045	−	14.6971i	−17.6525	−	20.4301i	16.4782	−	24.8940i
11.5	−2.73813	−	0.708980i	−4.61237	−	2.39291i	6.99469	+	3.88256i	0.577330	−	1.58620i	10.9327	+	9.82218i	−27.0016	−	4.76111i	−16.3997	−	15.5900i	15.5480	+	22.0740i	−2.70539	+	3.93391i
11.6	−2.66507	+	0.947300i	5.14914	−	0.697370i	6.20524	−	5.04925i	−1.80167	+	4.95006i	−13.0622	+	6.73633i	14.7819	+	2.60644i	−11.7543	+	19.3349i	26.0273	−	7.18172i	0.112404	−	14.8990i
11.7	−2.63308	−	1.03289i	5.16641	+	0.555160i	5.86626	+	5.43939i	6.86537	−	18.8624i	−13.0302	−	6.79813i	−18.0159	−	3.17669i	−9.82807	−	20.3816i	26.3836	+	5.73637i	−37.5600	+	42.5752i
11.8	−2.61271	+	1.08339i	2.79011	+	4.38352i	5.65252	−	5.66118i	−1.04436	+	2.86937i	−12.0388	−	8.43010i	−28.5377	−	5.03197i	−8.63512	+	20.9149i	−11.4306	+	24.4610i	−0.380029	−	8.62829i
11.9	−2.60460	−	1.10274i	2.16828	+	4.72213i	5.56791	+	5.74442i	−0.836765	+	2.29899i	−0.440216	−	14.6903i	22.6981	+	4.00229i	−8.16758	−	21.1019i	−17.5971	+	20.4779i	4.71464	−	5.06522i
11.10	−2.33178	+	1.60087i	−4.92086	−	1.66888i	2.87442	−	7.46577i	3.67143	−	10.0872i	14.1460	−	3.98618i	−6.04634	−	1.06613i	5.24922	+	22.0101i	21.4296	+	16.4247i	7.58728	+	29.3985i
11.11	−2.10858	+	1.88517i	−1.35776	−	5.01562i	0.892234	−	7.95009i	−5.18482	+	14.2452i	12.3183	+	8.01624i	−9.21752	−	1.62530i	13.1060	+	18.4454i	−23.3130	+	13.6200i	−15.9220	−	39.8114i
11.12	−2.10574	−	1.88834i	−3.74172	−	3.60549i	0.868318	+	7.95274i	−1.60571	+	4.41165i	1.07071	+	14.6579i	23.1356	+	4.07942i	13.1890	−	18.3861i	1.00093	+	26.9814i	11.7119	−	6.25768i
11.13	−2.04068	−	1.95848i	−2.83464	+	4.35486i	0.328747	+	7.99324i	−6.07198	+	16.6826i	14.3135	−	3.33532i	−22.8171	−	4.02326i	14.9837	−	16.9555i	−10.9297	−	24.6889i	45.0635	−	22.1521i
11.14	−1.88673	+	2.10719i	2.88986	−	4.31841i	−0.880530	−	7.95139i	3.28651	−	9.02962i	3.64735	+	14.2372i	−18.0956	−	3.19074i	18.4164	+	13.1467i	−10.2974	−	24.9592i	12.8264	+	23.9617i
11.15	−1.88377	−	2.10984i	−4.43306	+	2.71072i	−0.902841	+	7.94889i	5.32629	−	14.6339i	14.0700	+	4.24668i	6.67869	+	1.17763i	18.4716	−	13.0690i	12.3040	−	24.0335i	−40.9086	+	16.3292i
11.16	−1.76579	−	2.20953i	4.72349	−	2.16532i	−1.76401	+	7.80309i	−1.80584	+	4.96151i	−13.1250	−	6.61318i	9.40209	+	1.65784i	20.3560	−	9.88097i	17.6228	−	20.4558i	14.1513	−	4.77091i
11.17	−1.74755	+	2.22397i	−2.88986	+	4.31841i	−1.89211	−	7.77303i	3.28651	−	9.02962i	−4.55384	−	13.9736i	18.0956	+	3.19074i	20.5936	+	9.37578i	−10.2974	−	24.9592i	14.3383	+	23.0889i
11.18	−1.49038	+	2.40390i	1.35776	+	5.01562i	−3.55752	−	7.16548i	−5.18482	+	14.2452i	−14.0807	−	4.21127i	9.21752	+	1.62530i	22.5272	+	2.12738i	−23.3130	+	13.6200i	−26.5167	−	33.6946i
11.19	−1.17164	+	2.57435i	4.92086	+	1.66888i	−5.25451	−	6.03242i	3.67143	−	10.0872i	−10.0618	+	10.7127i	6.04634	+	1.06613i	21.6859	−	6.45911i	21.4296	+	16.4247i	21.6662	+	21.2701i
11.20	−1.11352	−	2.60001i	−0.629751	−	5.15785i	−5.52015	+	5.79033i	4.68740	−	12.8785i	−12.7092	+	7.38072i	−21.3342	−	3.76180i	21.2017	+	7.90483i	−26.2068	+	6.49632i	−38.7038	+	2.15317i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
27.f	odd	18	1	inner
108.l	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	108.4.l.a	✓	312
4.b	odd	2	1	inner	108.4.l.a	✓	312
27.f	odd	18	1	inner	108.4.l.a	✓	312
108.l	even	18	1	inner	108.4.l.a	✓	312

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
108.4.l.a	✓	312	1.a	even	1	1	trivial
108.4.l.a	✓	312	4.b	odd	2	1	inner
108.4.l.a	✓	312	27.f	odd	18	1	inner
108.4.l.a	✓	312	108.l	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(108, [\chi])\).