Newform orbit 891.2.u.e

• Label: 891.2.u.e
• Level: $891$
• Weight: $2$
• Character orbit: 891.u
• Analytic conductor: $7.115$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.11467082010\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(8\) over \(\Q(\zeta_{30})\)
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
107.1	−0.269800	−	2.56697i		0		−4.56025	+	0.969312i	0.460024	+	0.0483504i		0		1.41721	−	1.27606i	2.12333	+	6.53495i		0			−	1.19391i
107.2	−0.206165	−	1.96152i		0		−1.84878	+	0.392970i	0.935625	+	0.0983382i		0		−2.23753	+	2.01468i	−0.0669928	−	0.206183i		0			−	1.85553i
107.3	−0.106570	−	1.01395i		0		0.939559	−	0.199709i	−3.08748	−	0.324507i		0		3.11115	−	2.80129i	−0.932731	−	2.87065i		0				3.16513i
107.4	−0.0667948	−	0.635510i		0		1.55688	−	0.330926i	2.44156	+	0.256618i		0		−0.543595	+	0.489455i	−0.709229	−	2.18278i		0			−	1.56878i
107.5	0.0667948	+	0.635510i		0		1.55688	−	0.330926i	−2.44156	−	0.256618i		0		−0.543595	+	0.489455i	0.709229	+	2.18278i		0			−	1.56878i
107.6	0.106570	+	1.01395i		0		0.939559	−	0.199709i	3.08748	+	0.324507i		0		3.11115	−	2.80129i	0.932731	+	2.87065i		0				3.16513i
107.7	0.206165	+	1.96152i		0		−1.84878	+	0.392970i	−0.935625	−	0.0983382i		0		−2.23753	+	2.01468i	0.0669928	+	0.206183i		0			−	1.85553i
107.8	0.269800	+	2.56697i		0		−4.56025	+	0.969312i	−0.460024	−	0.0483504i		0		1.41721	−	1.27606i	−2.12333	−	6.53495i		0			−	1.19391i
134.1	−2.66757	+	0.567010i		0		4.96736	−	2.21161i	−0.462252	+	2.17472i		0		−3.33344	−	0.350359i	−7.58414	+	5.51020i		0			−	6.06334i
134.2	−1.64032	+	0.348661i		0		0.741992	−	0.330356i	0.314203	−	1.47821i		0		−4.09794	−	0.430711i	1.61147	−	1.17080i		0				2.53429i
134.3	−1.14283	+	0.242916i		0		−0.580043	+	0.258252i	−0.0549699	+	0.258613i		0		1.44175	+	0.151534i	2.49060	−	1.80953i		0			−	0.308903i
134.4	−0.607139	+	0.129051i		0		−1.47513	+	0.656769i	−0.776244	+	3.65194i		0		2.20625	+	0.231886i	1.81517	−	1.31880i		0			−	2.31741i
134.5	0.607139	−	0.129051i		0		−1.47513	+	0.656769i	0.776244	−	3.65194i		0		2.20625	+	0.231886i	−1.81517	+	1.31880i		0			−	2.31741i
134.6	1.14283	−	0.242916i		0		−0.580043	+	0.258252i	0.0549699	−	0.258613i		0		1.44175	+	0.151534i	−2.49060	+	1.80953i		0			−	0.308903i
134.7	1.64032	−	0.348661i		0		0.741992	−	0.330356i	−0.314203	+	1.47821i		0		−4.09794	−	0.430711i	−1.61147	+	1.17080i		0				2.53429i
134.8	2.66757	−	0.567010i		0		4.96736	−	2.21161i	0.462252	−	2.17472i		0		−3.33344	−	0.350359i	7.58414	−	5.51020i		0			−	6.06334i
215.1	−1.82483	+	2.02668i		0		−0.568369	−	5.40767i	1.65224	−	1.48768i		0		1.36330	−	3.06202i	7.58414	+	5.51020i		0				6.06334i
215.2	−1.12211	+	1.24623i		0		−0.0848992	−	0.807762i	−1.12307	+	1.01121i		0		1.67596	−	3.76427i	−1.61147	−	1.17080i		0			−	2.53429i
215.3	−0.781785	+	0.868260i		0		0.0663688	+	0.631457i	0.196480	−	0.176912i		0		−0.589641	+	1.32436i	−2.49060	−	1.80953i		0				0.308903i
215.4	−0.415331	+	0.461272i		0		0.168785	+	1.60588i	2.77455	−	2.49822i		0		−0.902304	+	2.02661i	−1.81517	−	1.31880i		0				2.31741i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
9.c	even	3	1	inner
9.d	odd	6	1	inner
11.d	odd	10	1	inner
33.f	even	10	1	inner
99.o	odd	30	1	inner
99.p	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	891.2.u.e		64
3.b	odd	2	1	inner	891.2.u.e		64
9.c	even	3	1		297.2.k.a	✓	32
9.c	even	3	1	inner	891.2.u.e		64
9.d	odd	6	1		297.2.k.a	✓	32
9.d	odd	6	1	inner	891.2.u.e		64
11.d	odd	10	1	inner	891.2.u.e		64
33.f	even	10	1	inner	891.2.u.e		64
99.o	odd	30	1		297.2.k.a	✓	32
99.o	odd	30	1	inner	891.2.u.e		64
99.p	even	30	1		297.2.k.a	✓	32
99.p	even	30	1	inner	891.2.u.e		64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
297.2.k.a	✓	32	9.c	even	3	1
297.2.k.a	✓	32	9.d	odd	6	1
297.2.k.a	✓	32	99.o	odd	30	1
297.2.k.a	✓	32	99.p	even	30	1
891.2.u.e		64	1.a	even	1	1	trivial
891.2.u.e		64	3.b	odd	2	1	inner
891.2.u.e		64	9.c	even	3	1	inner
891.2.u.e		64	9.d	odd	6	1	inner
891.2.u.e		64	11.d	odd	10	1	inner
891.2.u.e		64	33.f	even	10	1	inner
891.2.u.e		64	99.o	odd	30	1	inner
891.2.u.e		64	99.p	even	30	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^64 - 12*T2^62 + 43*T2^60 + 264*T2^58 - 4176*T2^56 + 35880*T2^54 - 105951*T2^52 - 941838*T2^50 + 11850128*T2^48 - 31809282*T2^46 - 67298988*T2^44 + 732769584*T2^42 - 1858140400*T2^40 + 1311445884*T2^38 + 10906466614*T2^36 - 69222053166*T2^34 + 196749439941*T2^32 - 242942898846*T2^30 + 118821814034*T2^28 + 118833167214*T2^26 - 426564119500*T2^24 + 579183063954*T2^22 - 137734466928*T2^20 - 438823166142*T2^18 + 539503505588*T2^16 - 134741476848*T2^14 - 33712887021*T2^12 + 36719468280*T2^10 - 12626632656*T2^8 + 2801321094*T2^6 + 837948353*T2^4 - 818461182*T2^2 + 214358881