Newform orbit 945.2.u.a

• Label: 945.2.u.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.u
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(44\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 38 q^{4} + 6 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1	−1.35415	−	2.34546i		0		−2.66745	+	4.62015i	2.11290	−	0.731888i		0		1.60604	−	2.10253i	9.03188				0		−4.57779	−	3.96463i
89.2	−1.28800	−	2.23088i		0		−2.31788	+	4.01469i	−0.488384	−	2.18208i		0		2.15932	+	1.52884i	6.78974				0		−4.23893	+	3.90005i
89.3	−1.26586	−	2.19253i		0		−2.20480	+	3.81882i	−1.14318	+	1.92175i		0		1.80040	+	1.93870i	6.10041				0		5.66061	+	0.0737875i
89.4	−1.23016	−	2.13070i		0		−2.02658	+	3.51014i	2.13577	−	0.662193i		0		−2.39641	+	1.12126i	5.05144				0		−4.03827	−	3.73607i
89.5	−1.14897	−	1.99008i		0		−1.64028	+	2.84105i	−1.90726	+	1.16720i		0		−2.44187	+	1.01847i	2.94267				0		4.51421	+	2.45453i
89.6	−1.08083	−	1.87205i		0		−1.33638	+	2.31468i	1.85798	+	1.24416i		0		0.599782	+	2.57687i	1.45428				0		0.320967	−	4.82294i
89.7	−1.03259	−	1.78850i		0		−1.13248	+	1.96151i	−1.44626	−	1.70539i		0		0.162008	−	2.64079i	0.547180				0		−1.55669	+	4.34759i
89.8	−1.02260	−	1.77120i		0		−1.09143	+	1.89041i	0.00270873	+	2.23607i		0		1.69883	−	2.02829i	0.373988				0		3.95775	−	2.29140i
89.9	−1.00105	−	1.73387i		0		−1.00421	+	1.73934i	−0.439789	−	2.19239i		0		−2.40459	−	1.10361i	0.0168431				0		−3.36108	+	2.95723i
89.10	−0.851246	−	1.47440i		0		−0.449240	+	0.778107i	−2.23006	−	0.163754i		0		−2.57388	+	0.612504i	−1.87533				0		1.65689	+	3.42740i
89.11	−0.754840	−	1.30742i		0		−0.139566	+	0.241735i	1.87872	+	1.21261i		0		−1.79617	−	1.94262i	−2.59796				0		0.167261	−	3.37160i
89.12	−0.686620	−	1.18926i		0		0.0571066	−	0.0989115i	−2.03494	+	0.926840i		0		2.64486	−	0.0687428i	−2.90332				0		2.49948	+	1.78368i
89.13	−0.665500	−	1.15268i		0		0.114220	−	0.197834i	1.38997	−	1.75157i		0		−1.25852	+	2.32726i	−2.96605				0		−2.94402	−	0.436517i
89.14	−0.603467	−	1.04524i		0		0.271654	−	0.470519i	0.171693	+	2.22947i		0		−0.716364	−	2.54692i	−3.06961				0		2.22671	−	1.52487i
89.15	−0.601450	−	1.04174i		0		0.276517	−	0.478941i	−1.70560	−	1.44600i		0		0.552728	+	2.58737i	−3.07104				0		−0.480530	+	2.64649i
89.16	−0.466107	−	0.807321i		0		0.565488	−	0.979455i	1.03266	−	1.98333i		0		2.46700	−	0.955995i	−2.91874				0		−2.08252	+	0.0907533i
89.17	−0.413705	−	0.716558i		0		0.657696	−	1.13916i	2.23428	−	0.0894268i		0		1.49622	+	2.18205i	−2.74319				0		−0.988412	−	1.56399i
89.18	−0.293005	−	0.507499i		0		0.828297	−	1.43465i	0.212444	+	2.22595i		0		−2.62667	+	0.317199i	−2.14280				0		1.06742	−	0.760030i
89.19	−0.252360	−	0.437100i		0		0.872629	−	1.51144i	1.06742	−	1.96485i		0		−1.93769	−	1.80149i	−1.89030				0		−1.12821	+	0.0292802i
89.20	−0.243540	−	0.421824i		0		0.881376	−	1.52659i	2.06439	+	0.859249i		0		2.62390	−	0.339358i	−1.83276				0		−0.140309	−	1.08007i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
63.s	even	6	1	inner
315.u	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.u.a		88
3.b	odd	2	1		315.2.u.a	✓	88
5.b	even	2	1	inner	945.2.u.a		88
7.d	odd	6	1		945.2.bq.a		88
9.c	even	3	1		315.2.bq.a	yes	88
9.d	odd	6	1		945.2.bq.a		88
15.d	odd	2	1		315.2.u.a	✓	88
21.g	even	6	1		315.2.bq.a	yes	88
35.i	odd	6	1		945.2.bq.a		88
45.h	odd	6	1		945.2.bq.a		88
45.j	even	6	1		315.2.bq.a	yes	88
63.k	odd	6	1		315.2.u.a	✓	88
63.s	even	6	1	inner	945.2.u.a		88
105.p	even	6	1		315.2.bq.a	yes	88
315.u	even	6	1	inner	945.2.u.a		88
315.bn	odd	6	1		315.2.u.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
315.2.u.a	✓	88	3.b	odd	2	1
315.2.u.a	✓	88	15.d	odd	2	1
315.2.u.a	✓	88	63.k	odd	6	1
315.2.u.a	✓	88	315.bn	odd	6	1
315.2.bq.a	yes	88	9.c	even	3	1
315.2.bq.a	yes	88	21.g	even	6	1
315.2.bq.a	yes	88	45.j	even	6	1
315.2.bq.a	yes	88	105.p	even	6	1
945.2.u.a		88	1.a	even	1	1	trivial
945.2.u.a		88	5.b	even	2	1	inner
945.2.u.a		88	63.s	even	6	1	inner
945.2.u.a		88	315.u	even	6	1	inner
945.2.bq.a		88	7.d	odd	6	1
945.2.bq.a		88	9.d	odd	6	1
945.2.bq.a		88	35.i	odd	6	1
945.2.bq.a		88	45.h	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(945, [\chi])\).