Newform orbit 111.3.l.b

• Label: 111.3.l.b
• Level: $111$
• Weight: $3$
• Character orbit: 111.l
• Analytic conductor: $3.025$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	111.l (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.02453093440\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{2} + 36 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} - 36 q^{8} + 36 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
82.1	−3.81682	−	1.02271i	1.50000	+	0.866025i	10.0581	+	5.80704i	3.12011	−	0.836031i	−4.83954	−	4.83954i	−4.42663	+	7.66714i	−21.2746	−	21.2746i	1.50000	+	2.59808i	−12.7639
82.2	−2.51039	−	0.672656i	1.50000	+	0.866025i	2.38548	+	1.37726i	−2.86514	+	0.767711i	−3.18304	−	3.18304i	4.00759	−	6.94135i	2.28887	+	2.28887i	1.50000	+	2.59808i	7.70901
82.3	−0.839390	−	0.224914i	1.50000	+	0.866025i	−2.81011	−	1.62242i	−2.87694	+	0.770875i	−1.06430	−	1.06430i	−5.46857	+	9.47184i	4.45178	+	4.45178i	1.50000	+	2.59808i	2.58826
82.4	−0.118812	−	0.0318357i	1.50000	+	0.866025i	−3.45100	−	1.99244i	7.22425	−	1.93573i	−0.150648	−	0.150648i	0.350980	−	0.607914i	0.694498	+	0.694498i	1.50000	+	2.59808i	−0.919956
82.5	2.32451	+	0.622850i	1.50000	+	0.866025i	1.55129	+	0.895636i	3.55969	−	0.953815i	2.94736	+	2.94736i	1.46050	−	2.52967i	−3.75850	−	3.75850i	1.50000	+	2.59808i	8.86860
82.6	3.09488	+	0.829271i	1.50000	+	0.866025i	5.42650	+	3.13299i	−3.56389	+	0.954941i	3.92415	+	3.92415i	−1.12003	+	1.93996i	5.13384	+	5.13384i	1.50000	+	2.59808i	−11.8217
88.1	−3.81682	+	1.02271i	1.50000	−	0.866025i	10.0581	−	5.80704i	3.12011	+	0.836031i	−4.83954	+	4.83954i	−4.42663	−	7.66714i	−21.2746	+	21.2746i	1.50000	−	2.59808i	−12.7639
88.2	−2.51039	+	0.672656i	1.50000	−	0.866025i	2.38548	−	1.37726i	−2.86514	−	0.767711i	−3.18304	+	3.18304i	4.00759	+	6.94135i	2.28887	−	2.28887i	1.50000	−	2.59808i	7.70901
88.3	−0.839390	+	0.224914i	1.50000	−	0.866025i	−2.81011	+	1.62242i	−2.87694	−	0.770875i	−1.06430	+	1.06430i	−5.46857	−	9.47184i	4.45178	−	4.45178i	1.50000	−	2.59808i	2.58826
88.4	−0.118812	+	0.0318357i	1.50000	−	0.866025i	−3.45100	+	1.99244i	7.22425	+	1.93573i	−0.150648	+	0.150648i	0.350980	+	0.607914i	0.694498	−	0.694498i	1.50000	−	2.59808i	−0.919956
88.5	2.32451	−	0.622850i	1.50000	−	0.866025i	1.55129	−	0.895636i	3.55969	+	0.953815i	2.94736	−	2.94736i	1.46050	+	2.52967i	−3.75850	+	3.75850i	1.50000	−	2.59808i	8.86860
88.6	3.09488	−	0.829271i	1.50000	−	0.866025i	5.42650	−	3.13299i	−3.56389	−	0.954941i	3.92415	−	3.92415i	−1.12003	−	1.93996i	5.13384	−	5.13384i	1.50000	−	2.59808i	−11.8217
97.1	−0.693785	−	2.58924i	1.50000	−	0.866025i	−2.75873	+	1.59276i	−0.209120	+	0.780447i	−3.28303	−	3.28303i	−3.61609	−	6.26326i	−1.54383	−	1.54383i	1.50000	−	2.59808i	2.16585
97.2	−0.682073	−	2.54553i	1.50000	−	0.866025i	−2.55040	+	1.47247i	2.05541	−	7.67090i	−3.22760	−	3.22760i	4.48853	+	7.77437i	−1.96605	−	1.96605i	1.50000	−	2.59808i	−20.9284
97.3	−0.103369	−	0.385779i	1.50000	−	0.866025i	3.32596	−	1.92024i	−2.38266	+	8.89221i	−0.489148	−	0.489148i	6.18137	+	10.7065i	−2.21423	−	2.21423i	1.50000	−	2.59808i	3.67672
97.4	−0.0210891	−	0.0787054i	1.50000	−	0.866025i	3.45835	−	1.99668i	0.222135	−	0.829019i	−0.0997945	−	0.0997945i	−2.82588	−	4.89456i	−0.460548	−	0.460548i	1.50000	−	2.59808i	−0.0699329
97.5	0.544686	+	2.03280i	1.50000	−	0.866025i	−0.371475	+	0.214471i	1.21483	−	4.53380i	2.57748	+	2.57748i	1.71728	+	2.97442i	5.31413	+	5.31413i	1.50000	−	2.59808i	9.87799
97.6	0.821656	+	3.06646i	1.50000	−	0.866025i	−5.26396	+	3.03915i	−1.49867	+	5.59311i	3.88812	+	3.88812i	−0.749067	−	1.29742i	−4.66537	−	4.66537i	1.50000	−	2.59808i	−18.3824
103.1	−0.693785	+	2.58924i	1.50000	+	0.866025i	−2.75873	−	1.59276i	−0.209120	−	0.780447i	−3.28303	+	3.28303i	−3.61609	+	6.26326i	−1.54383	+	1.54383i	1.50000	+	2.59808i	2.16585
103.2	−0.682073	+	2.54553i	1.50000	+	0.866025i	−2.55040	−	1.47247i	2.05541	+	7.67090i	−3.22760	+	3.22760i	4.48853	−	7.77437i	−1.96605	+	1.96605i	1.50000	+	2.59808i	−20.9284

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
37.g	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	111.3.l.b	✓	24
3.b	odd	2	1		333.3.bb.b		24
37.g	odd	12	1	inner	111.3.l.b	✓	24
111.m	even	12	1		333.3.bb.b		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
111.3.l.b	✓	24	1.a	even	1	1	trivial
111.3.l.b	✓	24	37.g	odd	12	1	inner
333.3.bb.b		24	3.b	odd	2	1
333.3.bb.b		24	111.m	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 + 4*T2^23 - T2^22 - 8*T2^21 - 114*T2^20 - 562*T2^19 + 109*T2^18 + 930*T2^17 + 15276*T2^16 + 49376*T2^15 + 8839*T2^14 - 54288*T2^13 - 506524*T2^12 - 1313710*T2^11 + 298067*T2^10 + 245242*T2^9 + 11002484*T2^8 + 26725280*T2^7 + 23662329*T2^6 + 11043568*T2^5 + 3832438*T2^4 + 688014*T2^3 + 67563*T2^2 + 4290*T2 + 169