Newform orbit 444.2.w.c

• Label: 444.2.w.c
• Level: $444$
• Weight: $2$
• Character orbit: 444.w
• Analytic conductor: $3.545$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.w (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.54535784974\)
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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1		0		−1.73135	+	0.0491746i		0		1.41011	−	0.377837i		0		−1.43914	+	2.49267i		0		2.99516	−	0.170277i		0
29.2		0		−1.60047	+	0.662186i		0		−3.57638	+	0.958288i		0		2.07398	−	3.59224i		0		2.12302	−	2.11962i		0
29.3		0		−0.968941	+	1.43567i		0		2.72187	−	0.729323i		0		0.375954	−	0.651171i		0		−1.12231	−	2.78216i		0
29.4		0		−0.823090	−	1.52398i		0		−1.41011	+	0.377837i		0		−1.43914	+	2.49267i		0		−1.64505	+	2.50875i		0
29.5		0		−0.383307	+	1.68910i		0		−0.692004	+	0.185422i		0		−0.343865	+	0.595591i		0		−2.70615	−	1.29489i		0
29.6		0		−0.226766	−	1.71714i		0		3.57638	−	0.958288i		0		2.07398	−	3.59224i		0		−2.89715	+	0.778778i		0
29.7		0		0.758858	−	1.55696i		0		−2.72187	+	0.729323i		0		0.375954	−	0.651171i		0		−1.84827	−	2.36303i		0
29.8		0		1.13812	+	1.30564i		0		3.00933	−	0.806349i		0		−1.53295	+	2.65515i		0		−0.409384	+	2.97194i		0
29.9		0		1.27115	−	1.17651i		0		0.692004	−	0.185422i		0		−0.343865	+	0.595591i		0		0.231666	−	2.99104i		0
29.10		0		1.69977	+	0.332818i		0		−3.00933	+	0.806349i		0		−1.53295	+	2.65515i		0		2.77846	+	1.13143i		0
125.1		0		−1.73018	−	0.0805272i		0		−0.826027	+	3.08277i		0		−0.374858	−	0.649272i		0		2.98703	+	0.278653i		0
125.2		0		−1.48482	−	0.891801i		0		0.195309	−	0.728903i		0		1.65599	+	2.86827i		0		1.40938	+	2.64833i		0
125.3		0		−0.795350	+	1.53864i		0		0.826027	−	3.08277i		0		−0.374858	−	0.649272i		0		−1.73484	−	2.44752i		0
125.4		0		−0.526856	−	1.64998i		0		−0.425223	+	1.58695i		0		−1.24138	−	2.15014i		0		−2.44485	+	1.73860i		0
125.5		0		−0.0666873	−	1.73077i		0		0.967937	−	3.61239i		0		−0.200342	−	0.347003i		0		−2.99111	+	0.230840i		0
125.6		0		0.0299122	+	1.73179i		0		−0.195309	+	0.728903i		0		1.65599	+	2.86827i		0		−2.99821	+	0.103604i		0
125.7		0		1.10038	−	1.33759i		0		−0.662862	+	2.47384i		0		1.02662	+	1.77815i		0		−0.578306	−	2.94373i		0
125.8		0		1.16549	+	1.28126i		0		0.425223	−	1.58695i		0		−1.24138	−	2.15014i		0		−0.283247	+	2.98660i		0
125.9		0		1.46554	+	0.923136i		0		−0.967937	+	3.61239i		0		−0.200342	−	0.347003i		0		1.29564	+	2.70579i		0
125.10		0		1.70858	−	0.284165i		0		0.662862	−	2.47384i		0		1.02662	+	1.77815i		0		2.83850	−	0.971038i		0

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	444.2.w.c	✓	40
3.b	odd	2	1	inner	444.2.w.c	✓	40
37.g	odd	12	1	inner	444.2.w.c	✓	40
111.m	even	12	1	inner	444.2.w.c	✓	40

    

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(444, [\chi])\):

T5^40 - 350*T5^36 + 86031*T5^32 - 19116*T5^30 - 10350368*T5^28 + 2857248*T5^26 + 901746217*T5^24 - 302895396*T5^22 - 39779328330*T5^20 - 312292908*T5^18 + 1235784515841*T5^16 + 1042889434524*T5^14 - 6859295302212*T5^12 - 5330620367676*T5^10 + 33813610529931*T5^8 + 4674454416504*T5^6 - 9763983740178*T5^4 - 1292377355676*T5^2 + 2755377564489

T7^20 + 29*T7^18 + 32*T7^17 + 578*T7^16 + 708*T7^15 + 6437*T7^14 + 9132*T7^13 + 51946*T7^12 + 63816*T7^11 + 227317*T7^10 + 237004*T7^9 + 669273*T7^8 + 608452*T7^7 + 731824*T7^6 + 448768*T7^5 + 406816*T7^4 + 217344*T7^3 + 132096*T7^2 + 36864*T7 + 9216