Newform orbit 945.2.bq.a

• Label: 945.2.bq.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.bq
• 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.bq (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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 76 q^{4} + 3 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
719.1	−2.70830				0		5.33489			1.69028	+	1.46388i		0		1.01783	+	2.44214i	−9.03188				0		−4.57779	−	3.96463i
719.2	−2.57600				0		4.63577			1.64555	−	1.51399i		0		−2.40367	+	1.10561i	−6.78974				0		−4.23893	+	3.90005i
719.3	−2.53172				0		4.40959			−2.23588	−	0.0291453i		0		−2.57916	+	0.589845i	−6.10041				0		5.66061	+	0.0737875i
719.4	−2.46032				0		4.05317			1.64136	+	1.51853i		0		0.227160	−	2.63598i	−5.05144				0		−4.03827	−	3.73607i
719.5	−2.29795				0		3.28056			−1.96445	−	1.06814i		0		0.338914	−	2.62395i	−2.94267				0		4.51421	+	2.45453i
719.6	−2.16166				0		2.67276			−0.148482	+	2.23113i		0		−2.53153	−	0.769008i	−1.45428				0		0.320967	−	4.82294i
719.7	−2.06518				0		2.26496			0.753779	−	2.10519i		0		2.20598	+	1.46070i	−0.547180				0		−1.55669	+	4.34759i
719.8	−2.04520				0		2.18286			−1.93514	+	1.12038i		0		0.907139	+	2.48538i	−0.373988				0		3.95775	−	2.29140i
719.9	−2.00210				0		2.00841			1.67877	−	1.47706i		0		2.15805	−	1.53063i	−0.0168431				0		−3.36108	+	2.95723i
719.10	−1.70249				0		0.898480			−0.973217	−	2.01317i		0		0.756494	−	2.53529i	1.87533				0		1.65689	+	3.42740i
719.11	−1.50968				0		0.279131			−0.110792	+	2.23332i		0		2.58044	−	0.584218i	2.59796				0		0.167261	−	3.37160i
719.12	−1.37324				0		−0.114213			−1.82014	−	1.29889i		0		−1.26290	+	2.32489i	2.90332				0		2.49948	+	1.78368i
719.13	−1.33100				0		−0.228439			2.21189	+	0.327962i		0		−1.38620	−	2.25354i	2.96605				0		−2.94402	−	0.436517i
719.14	−1.20693				0		−0.543308			−1.84493	+	1.26342i		0		2.56388	+	0.653073i	3.06961				0		2.22671	−	1.52487i
719.15	−1.20290				0		−0.553033			0.399476	−	2.20010i		0		−2.51709	−	0.815010i	3.07104				0		−0.480530	+	2.64649i
719.16	−0.932214				0		−1.13098			2.23395	−	0.0973524i		0		−0.405582	+	2.61448i	2.91874				0		−2.08252	+	0.0907533i
719.17	−0.827410				0		−1.31539			1.19459	+	1.89023i		0		−2.63782	+	0.204740i	2.74319				0		−0.988412	−	1.56399i
719.18	−0.586009				0		−1.65659			−1.82151	+	1.29696i		0		1.03863	−	2.43336i	2.14280				0		1.06742	−	0.760030i
719.19	−0.504719				0		−1.74526			2.23532	−	0.0580128i		0		2.52898	−	0.777347i	1.89030				0		−1.12821	+	0.0292802i
719.20	−0.487080				0		−1.76275			0.288062	+	2.21744i		0		−1.01806	+	2.44204i	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.i	even	6	1	inner
315.bq	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.bq.a		88
3.b	odd	2	1		315.2.bq.a	yes	88
5.b	even	2	1	inner	945.2.bq.a		88
7.d	odd	6	1		945.2.u.a		88
9.c	even	3	1		315.2.u.a	✓	88
9.d	odd	6	1		945.2.u.a		88
15.d	odd	2	1		315.2.bq.a	yes	88
21.g	even	6	1		315.2.u.a	✓	88
35.i	odd	6	1		945.2.u.a		88
45.h	odd	6	1		945.2.u.a		88
45.j	even	6	1		315.2.u.a	✓	88
63.i	even	6	1	inner	945.2.bq.a		88
63.t	odd	6	1		315.2.bq.a	yes	88
105.p	even	6	1		315.2.u.a	✓	88
315.q	odd	6	1		315.2.bq.a	yes	88
315.bq	even	6	1	inner	945.2.bq.a		88

    

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

Hecke kernels

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