Newform orbit 185.2.l.a

• Label: 185.2.l.a
• Level: $185$
• Weight: $2$
• Character orbit: 185.l
• Analytic conductor: $1.477$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(1.47723243739\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 32 * q - 14 * q^4 + 3 * q^5 + 4 * q^9 + 6 * q^10 + 12 * q^11 + 12 * q^15 - 10 * q^16 - 33 * q^20 - 18 * q^21 - 42 * q^24 + 3 * q^25 - 12 * q^26 + 34 * q^30 + 28 * q^34 - 42 * q^35 + 20 * q^36 - 18 * q^39 - 11 * q^40 - 36 * q^41 - 42 * q^44 + 48 * q^46 + 4 * q^49 - 27 * q^50 + 66 * q^54 + 12 * q^55 + 18 * q^56 - 54 * q^61 + 112 * q^64 + 24 * q^65 - 30 * q^69 + 4 * q^70 + 18 * q^71 - 60 * q^74 - 36 * q^75 - 42 * q^79 - 16 * q^81 + 88 * q^84 + 18 * q^85 + 18 * q^86 + 54 * q^89 - 3 * q^90 - 36 * q^91 + 12 * q^94 - 6 * q^95 - 114 * q^96 - 72 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
64.1	−1.37455	+	2.38079i	0.585119	−	0.337819i	−2.77877	−	4.81298i	1.58452	−	1.57775i			1.85740i	0.330820	−	0.190999i	9.78006			−1.27176	+	2.20275i	1.57828	+	5.94111i
64.2	−1.09063	+	1.88903i	−1.99551	+	1.15211i	−1.37896	−	2.38842i	−1.98654	−	1.02647i		−	5.02610i	2.14000	−	1.23553i	1.65321			1.15471	−	2.00001i	4.10562	−	2.63314i
64.3	−1.04773	+	1.81473i	−0.704687	+	0.406851i	−1.19549	−	2.07065i	0.539667	+	2.16997i		−	1.70509i	−0.576485	+	0.332834i	0.819287			−1.16894	+	2.02467i	−4.50333	−	1.29420i
64.4	−0.812617	+	1.40749i	2.85067	−	1.64584i	−0.320694	−	0.555458i	2.21638	+	0.296090i			5.34974i	−2.57876	+	1.48885i	−2.20806			3.91756	−	6.78541i	−2.21781	+	2.87893i
64.5	−0.651283	+	1.12805i	1.59141	−	0.918801i	0.151662	+	0.262686i	−0.706929	−	2.12138i			2.39360i	3.85136	−	2.22358i	−3.00023			0.188392	−	0.326304i	2.85344	+	0.584163i
64.6	−0.584022	+	1.01156i	0.699972	−	0.404129i	0.317836	+	0.550508i	−2.20281	+	0.384248i			0.944081i	−3.36550	+	1.94307i	−3.07858			−1.17336	+	2.03232i	0.897799	−	2.45267i
64.7	−0.348901	+	0.604314i	−1.12874	+	0.651678i	0.756536	+	1.31036i	2.23270	−	0.122667i		−	0.909484i	1.73221	−	1.00009i	−2.45143			−0.650633	+	1.12693i	−0.704862	+	1.39205i
64.8	−0.161429	+	0.279603i	1.50202	−	0.867191i	0.947881	+	1.64178i	−0.584385	+	2.15835i			0.559959i	1.63357	−	0.943142i	−1.25778			0.00403875	−	0.00699531i	−0.509146	−	0.511817i
64.9	0.161429	−	0.279603i	−1.50202	+	0.867191i	0.947881	+	1.64178i	−2.16138	−	0.573085i			0.559959i	−1.63357	+	0.943142i	1.25778			0.00403875	−	0.00699531i	−0.509146	+	0.511817i
64.10	0.348901	−	0.604314i	1.12874	−	0.651678i	0.756536	+	1.31036i	1.22258	−	1.87224i		−	0.909484i	−1.73221	+	1.00009i	2.45143			−0.650633	+	1.12693i	−0.704862	−	1.39205i
64.11	0.584022	−	1.01156i	−0.699972	+	0.404129i	0.317836	+	0.550508i	−1.43417	+	1.71556i			0.944081i	3.36550	−	1.94307i	3.07858			−1.17336	+	2.03232i	0.897799	+	2.45267i
64.12	0.651283	−	1.12805i	−1.59141	+	0.918801i	0.151662	+	0.262686i	1.48370	+	1.67291i			2.39360i	−3.85136	+	2.22358i	3.00023			0.188392	−	0.326304i	2.85344	−	0.584163i
64.13	0.812617	−	1.40749i	−2.85067	+	1.64584i	−0.320694	−	0.555458i	0.851767	−	2.06748i			5.34974i	2.57876	−	1.48885i	2.20806			3.91756	−	6.78541i	−2.21781	−	2.87893i
64.14	1.04773	−	1.81473i	0.704687	−	0.406851i	−1.19549	−	2.07065i	−1.60941	−	1.55235i		−	1.70509i	0.576485	−	0.332834i	−0.819287			−1.16894	+	2.02467i	−4.50333	+	1.29420i
64.15	1.09063	−	1.88903i	1.99551	−	1.15211i	−1.37896	−	2.38842i	−0.104323	+	2.23363i		−	5.02610i	−2.14000	+	1.23553i	−1.65321			1.15471	−	2.00001i	4.10562	+	2.63314i
64.16	1.37455	−	2.38079i	−0.585119	+	0.337819i	−2.77877	−	4.81298i	2.15863	−	0.583362i			1.85740i	−0.330820	+	0.190999i	−9.78006			−1.27176	+	2.20275i	1.57828	−	5.94111i
159.1	−1.37455	−	2.38079i	0.585119	+	0.337819i	−2.77877	+	4.81298i	1.58452	+	1.57775i		−	1.85740i	0.330820	+	0.190999i	9.78006			−1.27176	−	2.20275i	1.57828	−	5.94111i
159.2	−1.09063	−	1.88903i	−1.99551	−	1.15211i	−1.37896	+	2.38842i	−1.98654	+	1.02647i			5.02610i	2.14000	+	1.23553i	1.65321			1.15471	+	2.00001i	4.10562	+	2.63314i
159.3	−1.04773	−	1.81473i	−0.704687	−	0.406851i	−1.19549	+	2.07065i	0.539667	−	2.16997i			1.70509i	−0.576485	−	0.332834i	0.819287			−1.16894	−	2.02467i	−4.50333	+	1.29420i
159.4	−0.812617	−	1.40749i	2.85067	+	1.64584i	−0.320694	+	0.555458i	2.21638	−	0.296090i		−	5.34974i	−2.57876	−	1.48885i	−2.20806			3.91756	+	6.78541i	−2.21781	−	2.87893i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
37.e	even	6	1	inner
185.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	185.2.l.a	✓	32
5.b	even	2	1	inner	185.2.l.a	✓	32
5.c	odd	4	2		925.2.n.e		32
37.e	even	6	1	inner	185.2.l.a	✓	32
185.l	even	6	1	inner	185.2.l.a	✓	32
185.r	odd	12	2		925.2.n.e		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.2.l.a	✓	32	1.a	even	1	1	trivial
185.2.l.a	✓	32	5.b	even	2	1	inner
185.2.l.a	✓	32	37.e	even	6	1	inner
185.2.l.a	✓	32	185.l	even	6	1	inner
925.2.n.e		32	5.c	odd	4	2
925.2.n.e		32	185.r	odd	12	2

Hecke kernels

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