Newform orbit 111.2.m.a

• Label: 111.2.m.a
• Level: $111$
• Weight: $2$
• Character orbit: 111.m
• Analytic conductor: $0.886$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.m (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.886339462436\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(10\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 6 q^{3} - 12 q^{4} - 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
8.1	−0.683439	+	2.55063i	0.839686	+	1.51490i	−4.30657	−	2.48640i	−0.283720	−	1.05886i	−4.43783	+	1.10639i	−1.64962	+	2.85722i	5.55078	−	5.55078i	−1.58985	+	2.54408i	2.89466
8.2	−0.533449	+	1.99086i	−0.511133	−	1.65491i	−1.94690	−	1.12404i	0.925921	+	3.45558i	3.56736	−	0.134781i	−1.01771	+	1.76272i	0.361558	−	0.361558i	−2.47749	+	1.69176i	−7.37351
8.3	−0.416454	+	1.55423i	1.64320	−	0.547611i	−0.510140	−	0.294529i	−0.0381491	−	0.142374i	0.166793	+	2.78197i	0.640536	−	1.10944i	−1.60533	+	1.60533i	2.40024	−	1.79967i	0.237169
8.4	−0.206569	+	0.770928i	−1.03906	+	1.38577i	1.18039	+	0.681500i	−0.142078	−	0.530243i	−0.853691	−	1.08730i	−1.23437	+	2.13800i	−1.89794	+	1.89794i	−0.840721	−	2.87979i	0.438128
8.5	−0.138198	+	0.515763i	−0.906220	−	1.47606i	1.48514	+	0.857445i	−0.874215	−	3.26261i	0.886538	−	0.263405i	1.02911	−	1.78247i	−1.40261	+	1.40261i	−1.35753	+	2.67528i	1.80355
8.6	0.138198	−	0.515763i	−1.73142	−	0.0467770i	1.48514	+	0.857445i	0.874215	+	3.26261i	−0.263405	+	0.886538i	1.02911	−	1.78247i	1.40261	−	1.40261i	2.99562	+	0.161981i	1.80355
8.7	0.206569	−	0.770928i	0.680584	−	1.59274i	1.18039	+	0.681500i	0.142078	+	0.530243i	−1.08730	−	0.853691i	−1.23437	+	2.13800i	1.89794	−	1.89794i	−2.07361	−	2.16798i	0.438128
8.8	0.416454	−	1.55423i	0.347357	+	1.69686i	−0.510140	−	0.294529i	0.0381491	+	0.142374i	2.78197	+	0.166793i	0.640536	−	1.10944i	1.60533	−	1.60533i	−2.75869	+	1.17883i	0.237169
8.9	0.533449	−	1.99086i	−1.68876	+	0.384803i	−1.94690	−	1.12404i	−0.925921	−	3.45558i	−0.134781	+	3.56736i	−1.01771	+	1.76272i	−0.361558	+	0.361558i	2.70385	−	1.29968i	−7.37351
8.10	0.683439	−	2.55063i	1.73179	−	0.0302610i	−4.30657	−	2.48640i	0.283720	+	1.05886i	1.10639	−	4.43783i	−1.64962	+	2.85722i	−5.55078	+	5.55078i	2.99817	−	0.104811i	2.89466
14.1	−0.683439	−	2.55063i	0.839686	−	1.51490i	−4.30657	+	2.48640i	−0.283720	+	1.05886i	−4.43783	−	1.10639i	−1.64962	−	2.85722i	5.55078	+	5.55078i	−1.58985	−	2.54408i	2.89466
14.2	−0.533449	−	1.99086i	−0.511133	+	1.65491i	−1.94690	+	1.12404i	0.925921	−	3.45558i	3.56736	+	0.134781i	−1.01771	−	1.76272i	0.361558	+	0.361558i	−2.47749	−	1.69176i	−7.37351
14.3	−0.416454	−	1.55423i	1.64320	+	0.547611i	−0.510140	+	0.294529i	−0.0381491	+	0.142374i	0.166793	−	2.78197i	0.640536	+	1.10944i	−1.60533	−	1.60533i	2.40024	+	1.79967i	0.237169
14.4	−0.206569	−	0.770928i	−1.03906	−	1.38577i	1.18039	−	0.681500i	−0.142078	+	0.530243i	−0.853691	+	1.08730i	−1.23437	−	2.13800i	−1.89794	−	1.89794i	−0.840721	+	2.87979i	0.438128
14.5	−0.138198	−	0.515763i	−0.906220	+	1.47606i	1.48514	−	0.857445i	−0.874215	+	3.26261i	0.886538	+	0.263405i	1.02911	+	1.78247i	−1.40261	−	1.40261i	−1.35753	−	2.67528i	1.80355
14.6	0.138198	+	0.515763i	−1.73142	+	0.0467770i	1.48514	−	0.857445i	0.874215	−	3.26261i	−0.263405	−	0.886538i	1.02911	+	1.78247i	1.40261	+	1.40261i	2.99562	−	0.161981i	1.80355
14.7	0.206569	+	0.770928i	0.680584	+	1.59274i	1.18039	−	0.681500i	0.142078	−	0.530243i	−1.08730	+	0.853691i	−1.23437	−	2.13800i	1.89794	+	1.89794i	−2.07361	+	2.16798i	0.438128
14.8	0.416454	+	1.55423i	0.347357	−	1.69686i	−0.510140	+	0.294529i	0.0381491	−	0.142374i	2.78197	−	0.166793i	0.640536	+	1.10944i	1.60533	+	1.60533i	−2.75869	−	1.17883i	0.237169
14.9	0.533449	+	1.99086i	−1.68876	−	0.384803i	−1.94690	+	1.12404i	−0.925921	+	3.45558i	−0.134781	−	3.56736i	−1.01771	−	1.76272i	−0.361558	−	0.361558i	2.70385	+	1.29968i	−7.37351
14.10	0.683439	+	2.55063i	1.73179	+	0.0302610i	−4.30657	+	2.48640i	0.283720	−	1.05886i	1.10639	+	4.43783i	−1.64962	−	2.85722i	−5.55078	−	5.55078i	2.99817	+	0.104811i	2.89466

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
37.g	odd	12	1	inner
111.m	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	111.2.m.a	✓	40
3.b	odd	2	1	inner	111.2.m.a	✓	40
37.g	odd	12	1	inner	111.2.m.a	✓	40
111.m	even	12	1	inner	111.2.m.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
111.2.m.a	✓	40	1.a	even	1	1	trivial
111.2.m.a	✓	40	3.b	odd	2	1	inner
111.2.m.a	✓	40	37.g	odd	12	1	inner
111.2.m.a	✓	40	111.m	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(111, [\chi])\).