Newform orbit 456.2.bm.a

• Label: 456.2.bm.a
• Level: $456$
• Weight: $2$
• Character orbit: 456.bm
• Analytic conductor: $3.641$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.64117833217\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(10\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
41.1		0		−1.72277	−	0.179059i		0		−1.70062	−	0.299865i		0		1.13747	+	1.97015i		0		2.93588	+	0.616956i		0
41.2		0		−1.37442	+	1.05403i		0		2.36417	+	0.416867i		0		−2.12924	−	3.68795i		0		0.778040	−	2.89735i		0
41.3		0		−1.30319	−	1.14092i		0		4.07516	+	0.718561i		0		0.904376	+	1.56643i		0		0.396593	+	2.97367i		0
41.4		0		−1.22013	−	1.22934i		0		−2.45783	−	0.433381i		0		−2.29577	−	3.97638i		0		−0.0225427	+	2.99992i		0
41.5		0		−0.745042	+	1.56362i		0		−0.726176	−	0.128044i		0		1.38478	+	2.39851i		0		−1.88983	−	2.32993i		0
41.6		0		0.597712	−	1.62565i		0		0.320800	+	0.0565656i		0		−0.0144179	−	0.0249726i		0		−2.28548	−	1.94334i		0
41.7		0		0.677725	+	1.59395i		0		−2.78114	−	0.490390i		0		−1.12097	−	1.94159i		0		−2.08138	+	2.16052i		0
41.8		0		1.17455	+	1.27297i		0		1.23805	+	0.218301i		0		−0.753669	−	1.30539i		0		−0.240883	+	2.99031i		0
41.9		0		1.68394	−	0.405410i		0		3.00241	+	0.529406i		0		−0.251171	−	0.435040i		0		2.67129	−	1.36537i		0
41.10		0		1.73163	−	0.0381668i		0		−3.33482	−	0.588019i		0		2.19892	+	3.80864i		0		2.99709	−	0.132181i		0
89.1		0		−1.72277	+	0.179059i		0		−1.70062	+	0.299865i		0		1.13747	−	1.97015i		0		2.93588	−	0.616956i		0
89.2		0		−1.37442	−	1.05403i		0		2.36417	−	0.416867i		0		−2.12924	+	3.68795i		0		0.778040	+	2.89735i		0
89.3		0		−1.30319	+	1.14092i		0		4.07516	−	0.718561i		0		0.904376	−	1.56643i		0		0.396593	−	2.97367i		0
89.4		0		−1.22013	+	1.22934i		0		−2.45783	+	0.433381i		0		−2.29577	+	3.97638i		0		−0.0225427	−	2.99992i		0
89.5		0		−0.745042	−	1.56362i		0		−0.726176	+	0.128044i		0		1.38478	−	2.39851i		0		−1.88983	+	2.32993i		0
89.6		0		0.597712	+	1.62565i		0		0.320800	−	0.0565656i		0		−0.0144179	+	0.0249726i		0		−2.28548	+	1.94334i		0
89.7		0		0.677725	−	1.59395i		0		−2.78114	+	0.490390i		0		−1.12097	+	1.94159i		0		−2.08138	−	2.16052i		0
89.8		0		1.17455	−	1.27297i		0		1.23805	−	0.218301i		0		−0.753669	+	1.30539i		0		−0.240883	−	2.99031i		0
89.9		0		1.68394	+	0.405410i		0		3.00241	−	0.529406i		0		−0.251171	+	0.435040i		0		2.67129	+	1.36537i		0
89.10		0		1.73163	+	0.0381668i		0		−3.33482	+	0.588019i		0		2.19892	−	3.80864i		0		2.99709	+	0.132181i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
57.j	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	456.2.bm.a	✓	60
3.b	odd	2	1		456.2.bm.b	yes	60
4.b	odd	2	1		912.2.cc.h		60
12.b	even	2	1		912.2.cc.g		60
19.f	odd	18	1		456.2.bm.b	yes	60
57.j	even	18	1	inner	456.2.bm.a	✓	60
76.k	even	18	1		912.2.cc.g		60
228.u	odd	18	1		912.2.cc.h		60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
456.2.bm.a	✓	60	1.a	even	1	1	trivial
456.2.bm.a	✓	60	57.j	even	18	1	inner
456.2.bm.b	yes	60	3.b	odd	2	1
456.2.bm.b	yes	60	19.f	odd	18	1
912.2.cc.g		60	12.b	even	2	1
912.2.cc.g		60	76.k	even	18	1
912.2.cc.h		60	4.b	odd	2	1
912.2.cc.h		60	228.u	odd	18	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^60 - 3*T5^58 - 36*T5^57 + 3*T5^56 + 78*T5^55 - 3824*T5^54 - 3324*T5^53 + 11229*T5^52 + 163044*T5^51 + 135261*T5^50 + 505380*T5^49 + 14939097*T5^48 + 5756682*T5^47 - 83843205*T5^46 - 230350254*T5^45 - 476859573*T5^44 - 874269756*T5^43 - 7949453093*T5^42 + 5649144918*T5^41 + 92699716845*T5^40 + 156631742124*T5^39 - 23640881484*T5^38 - 209974241874*T5^37 + 3964215596863*T5^36 + 3000687479406*T5^35 - 26222436212523*T5^34 - 59423844928020*T5^33 - 52350069052272*T5^32 + 108708774226998*T5^31 - 54304899190517*T5^30 + 333566778583080*T5^29 + 2631554858773872*T5^28 + 2894838907129026*T5^27 + 2817250851202254*T5^26 - 11103618365482662*T5^25 + 21149447948754716*T5^24 + 17783597595306990*T5^23 - 121591172688716916*T5^22 + 120523383723763920*T5^21 + 57605120016124515*T5^20 - 281141187738110700*T5^19 + 231901642401219796*T5^18 - 78491202303726864*T5^17 + 152825871867444351*T5^16 - 179755610450274936*T5^15 + 88621584574641669*T5^14 + 103857609293301426*T5^13 - 20468518160210583*T5^12 + 26680755070191132*T5^11 - 47293418811566952*T5^10 + 67482530495556984*T5^9 + 6787972846678848*T5^8 - 31801813639122816*T5^7 + 15785694062480064*T5^6 - 4189896784477440*T5^5 + 793954858887168*T5^4 - 156157407449088*T5^3 + 26306501197824*T5^2 - 1186330312704*T5 + 66324791296