Newform orbit 185.2.v.a

• Label: 185.2.v.a
• Level: $185$
• Weight: $2$
• Character orbit: 185.v
• Analytic conductor: $1.477$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.v (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.47723243739\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(16\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−0.430188	+	2.43972i	1.12805	−	0.198906i	−3.88777	−	1.41503i	−1.62031	+	1.54097i			2.83769i	1.92128	+	2.28969i	2.64739	−	4.58542i	−1.58614	+	0.577309i	−3.06249	−	4.61601i
4.2	−0.424622	+	2.40815i	−1.95789	+	0.345229i	−3.73949	−	1.36106i	−0.131730	−	2.23218i		−	4.86149i	−0.265922	−	0.316914i	2.42022	−	4.19194i	0.895083	−	0.325783i	5.43137	+	0.630608i
4.3	−0.391541	+	2.22054i	2.59680	−	0.457886i	−2.89811	−	1.05483i	1.60069	−	1.56134i			5.94558i	−0.639059	−	0.761600i	1.22222	−	2.11694i	3.71464	−	1.35202i	2.84028	+	4.16573i
4.4	−0.290576	+	1.64794i	−0.739987	+	0.130480i	−0.751873	−	0.273659i	−2.17943	+	0.500076i		−	1.25737i	−3.18694	−	3.79805i	−1.00391	+	1.73882i	−2.28852	+	0.832954i	−0.190803	−	3.73687i
4.5	−0.284304	+	1.61237i	−1.43078	+	0.252285i	−0.639514	−	0.232764i	1.92134	+	1.14388i		−	2.37867i	0.794560	+	0.946920i	−1.08012	+	1.87083i	−0.835589	+	0.304129i	−2.39059	+	2.77270i
4.6	−0.181851	+	1.03133i	1.62560	−	0.286637i	0.848817	+	0.308944i	−1.38855	−	1.75269i			1.72865i	1.72657	+	2.05765i	−1.52022	+	2.63310i	−0.258668	+	0.0941476i	2.06011	−	1.11332i
4.7	−0.0448121	+	0.254142i	−2.87442	+	0.506838i	1.81681	+	0.661263i	0.528279	−	2.17277i		−	0.753224i	1.46076	+	1.74086i	−0.507532	+	0.879071i	5.18634	−	1.88767i	0.528518	+	0.231624i
4.8	−0.0322691	+	0.183007i	0.566572	−	0.0999019i	1.84693	+	0.672229i	2.11760	−	0.718167i			0.106911i	−1.33240	−	1.58789i	−0.368452	+	0.638178i	−2.50805	+	0.912857i	0.0630966	+	0.410711i
4.9	0.0322691	−	0.183007i	−0.566572	+	0.0999019i	1.84693	+	0.672229i	−1.07497	+	1.96072i			0.106911i	1.33240	+	1.58789i	0.368452	−	0.638178i	−2.50805	+	0.912857i	0.324138	+	0.259999i
4.10	0.0448121	−	0.254142i	2.87442	−	0.506838i	1.81681	+	0.661263i	−2.23149	+	0.142956i		−	0.753224i	−1.46076	−	1.74086i	0.507532	−	0.879071i	5.18634	−	1.88767i	−0.0636668	+	0.573522i
4.11	0.181851	−	1.03133i	−1.62560	+	0.286637i	0.848817	+	0.308944i	−1.48495	−	1.67180i			1.72865i	−1.72657	−	2.05765i	1.52022	−	2.63310i	−0.258668	+	0.0941476i	−1.99422	+	1.22745i
4.12	0.284304	−	1.61237i	1.43078	−	0.252285i	−0.639514	−	0.232764i	0.792861	+	2.09078i		−	2.37867i	−0.794560	−	0.946920i	1.08012	−	1.87083i	−0.835589	+	0.304129i	3.59652	−	0.683965i
4.13	0.290576	−	1.64794i	0.739987	−	0.130480i	−0.751873	−	0.273659i	0.870933	−	2.05948i		−	1.25737i	3.18694	+	3.79805i	1.00391	−	1.73882i	−2.28852	+	0.832954i	−3.14083	−	2.03368i
4.14	0.391541	−	2.22054i	−2.59680	+	0.457886i	−2.89811	−	1.05483i	−1.81558	+	1.30525i			5.94558i	0.639059	+	0.761600i	−1.22222	+	2.11694i	3.71464	−	1.35202i	2.18749	+	4.54262i
4.15	0.424622	−	2.40815i	1.95789	−	0.345229i	−3.73949	−	1.36106i	−2.17540	−	0.517344i		−	4.86149i	0.265922	+	0.316914i	−2.42022	+	4.19194i	0.895083	−	0.325783i	−2.16956	+	5.01901i
4.16	0.430188	−	2.43972i	−1.12805	+	0.198906i	−3.88777	−	1.41503i	1.79892	−	1.32811i			2.83769i	−1.92128	−	2.28969i	−2.64739	+	4.58542i	−1.58614	+	0.577309i	−2.46633	−	4.96020i
99.1	−2.05127	+	1.72122i	1.45204	−	1.73048i	0.897813	−	5.09175i	−2.01069	+	0.978336i			6.04896i	−0.461702	−	1.26851i	4.24463	+	7.35191i	−0.365177	−	2.07102i	2.44053	−	5.46766i
99.2	−1.60232	+	1.34451i	−1.10176	+	1.31302i	0.412438	−	2.33905i	1.22797	−	1.86871i		−	3.58520i	−1.10353	−	3.03192i	0.392335	+	0.679545i	0.0107848	+	0.0611636i	0.544897	+	4.64530i
99.3	−1.58972	+	1.33394i	0.246630	−	0.293922i	0.400539	−	2.27157i	−1.03663	−	1.98126i			0.796243i	1.16480	+	3.20026i	0.318147	+	0.551046i	0.495381	+	2.80944i	4.29083	+	1.76687i
99.4	−1.27542	+	1.07021i	1.65654	−	1.97419i	0.134064	−	0.760312i	2.19645	+	0.419031i			4.29076i	0.0484108	+	0.133008i	−1.02224	−	1.77057i	−0.632347	−	3.58622i	−3.24986	+	1.81622i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
37.h	even	18	1	inner
185.v	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	185.2.v.a	✓	96
5.b	even	2	1	inner	185.2.v.a	✓	96
5.c	odd	4	2		925.2.bb.e		96
37.h	even	18	1	inner	185.2.v.a	✓	96
185.v	even	18	1	inner	185.2.v.a	✓	96
185.y	odd	36	2		925.2.bb.e		96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.2.v.a	✓	96	1.a	even	1	1	trivial
185.2.v.a	✓	96	5.b	even	2	1	inner
185.2.v.a	✓	96	37.h	even	18	1	inner
185.2.v.a	✓	96	185.v	even	18	1	inner
925.2.bb.e		96	5.c	odd	4	2
925.2.bb.e		96	185.y	odd	36	2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(185, [\chi])\).