Newform orbit 460.2.o.a

• Label: 460.2.o.a
• Level: $460$
• Weight: $2$
• Character orbit: 460.o
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $40$
• CM discriminant: -20
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(4\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−0.587486	−	1.28641i	−2.19630	+	0.644892i	−1.30972	+	1.51150i	−1.20891	+	1.88110i	2.11989	+	2.44649i	−4.60217	+	0.661692i	2.71386	+	0.796860i	1.88410	−	1.21083i	3.13009	+	0.450039i
19.2	−0.587486	−	1.28641i	3.32368	−	0.975920i	−1.30972	+	1.51150i	1.20891	−	1.88110i	−3.20805	−	3.70229i	−3.71125	+	0.533598i	2.71386	+	0.796860i	7.57066	−	4.86537i	−3.13009	−	0.450039i
19.3	0.587486	+	1.28641i	−3.32368	+	0.975920i	−1.30972	+	1.51150i	1.20891	−	1.88110i	−3.20805	−	3.70229i	3.71125	−	0.533598i	−2.71386	−	0.796860i	7.57066	−	4.86537i	3.13009	+	0.450039i
19.4	0.587486	+	1.28641i	2.19630	−	0.644892i	−1.30972	+	1.51150i	−1.20891	+	1.88110i	2.11989	+	2.44649i	4.60217	−	0.661692i	−2.71386	−	0.796860i	1.88410	−	1.21083i	−3.13009	−	0.450039i
79.1	−0.926113	−	1.06879i	−2.78960	−	1.79277i	−0.284630	+	1.97964i	−2.03400	−	0.928896i	0.667391	+	4.64180i	−0.518076	+	1.76441i	2.37942	−	1.52916i	3.32161	+	7.27330i	0.890917	+	3.03418i
79.2	−0.926113	−	1.06879i	1.23141	+	0.791378i	−0.284630	+	1.97964i	2.03400	+	0.928896i	−0.294605	−	2.04902i	1.19158	−	4.05815i	2.37942	−	1.52916i	−0.356159	−	0.779879i	−0.890917	−	3.03418i
79.3	0.926113	+	1.06879i	−1.23141	−	0.791378i	−0.284630	+	1.97964i	2.03400	+	0.928896i	−0.294605	−	2.04902i	−1.19158	+	4.05815i	−2.37942	+	1.52916i	−0.356159	−	0.779879i	0.890917	+	3.03418i
79.4	0.926113	+	1.06879i	2.78960	+	1.79277i	−0.284630	+	1.97964i	−2.03400	−	0.928896i	0.667391	+	4.64180i	0.518076	−	1.76441i	−2.37942	+	1.52916i	3.32161	+	7.27330i	−0.890917	−	3.03418i
99.1	−0.926113	+	1.06879i	−2.78960	+	1.79277i	−0.284630	−	1.97964i	−2.03400	+	0.928896i	0.667391	−	4.64180i	−0.518076	−	1.76441i	2.37942	+	1.52916i	3.32161	−	7.27330i	0.890917	−	3.03418i
99.2	−0.926113	+	1.06879i	1.23141	−	0.791378i	−0.284630	−	1.97964i	2.03400	−	0.928896i	−0.294605	+	2.04902i	1.19158	+	4.05815i	2.37942	+	1.52916i	−0.356159	+	0.779879i	−0.890917	+	3.03418i
99.3	0.926113	−	1.06879i	−1.23141	+	0.791378i	−0.284630	−	1.97964i	2.03400	−	0.928896i	−0.294605	+	2.04902i	−1.19158	−	4.05815i	−2.37942	−	1.52916i	−0.356159	+	0.779879i	0.890917	−	3.03418i
99.4	0.926113	−	1.06879i	2.78960	−	1.79277i	−0.284630	−	1.97964i	−2.03400	+	0.928896i	0.667391	−	4.64180i	0.518076	+	1.76441i	−2.37942	−	1.52916i	3.32161	−	7.27330i	−0.890917	+	3.03418i
159.1	−1.18971	−	0.764582i	−0.0739958	−	0.514652i	0.830830	+	1.81926i	0.629973	−	2.14549i	−0.305460	+	0.668863i	−0.858171	−	0.743609i	0.402527	−	2.79964i	2.61909	−	0.769034i	−2.38989	+	2.07085i
159.2	−1.18971	−	0.764582i	0.412623	+	2.86986i	0.830830	+	1.81926i	−0.629973	+	2.14549i	1.70334	−	3.72979i	−3.98826	−	3.45585i	0.402527	−	2.79964i	−5.18734	+	1.52314i	2.38989	−	2.07085i
159.3	1.18971	+	0.764582i	−0.412623	−	2.86986i	0.830830	+	1.81926i	−0.629973	+	2.14549i	1.70334	−	3.72979i	3.98826	+	3.45585i	−0.402527	+	2.79964i	−5.18734	+	1.52314i	−2.38989	+	2.07085i
159.4	1.18971	+	0.764582i	0.0739958	+	0.514652i	0.830830	+	1.81926i	0.629973	−	2.14549i	−0.305460	+	0.668863i	0.858171	+	0.743609i	−0.402527	+	2.79964i	2.61909	−	0.769034i	2.38989	−	2.07085i
199.1	−0.201264	+	1.39982i	−1.38389	−	3.03031i	−1.91899	−	0.563465i	1.68991	−	1.46431i	4.52041	−	1.32731i	2.67835	−	4.16759i	1.17497	−	2.57283i	−5.30301	+	6.12000i	1.70966	+	2.66028i
199.2	−0.201264	+	1.39982i	1.21668	+	2.66415i	−1.91899	−	0.563465i	−1.68991	+	1.46431i	−3.97421	+	1.16693i	−0.198162	+	0.308347i	1.17497	−	2.57283i	−3.65283	+	4.21559i	−1.70966	−	2.66028i
199.3	0.201264	−	1.39982i	−1.21668	−	2.66415i	−1.91899	−	0.563465i	−1.68991	+	1.46431i	−3.97421	+	1.16693i	0.198162	−	0.308347i	−1.17497	+	2.57283i	−3.65283	+	4.21559i	1.70966	+	2.66028i
199.4	0.201264	−	1.39982i	1.38389	+	3.03031i	−1.91899	−	0.563465i	1.68991	−	1.46431i	4.52041	−	1.32731i	−2.67835	+	4.16759i	−1.17497	+	2.57283i	−5.30301	+	6.12000i	−1.70966	−	2.66028i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
20.d	odd	2	1	CM by \(\Q(\sqrt{-5}) \)
4.b	odd	2	1	inner
5.b	even	2	1	inner
23.d	odd	22	1	inner
92.h	even	22	1	inner
115.i	odd	22	1	inner
460.o	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	460.2.o.a	✓	40
4.b	odd	2	1	inner	460.2.o.a	✓	40
5.b	even	2	1	inner	460.2.o.a	✓	40
20.d	odd	2	1	CM	460.2.o.a	✓	40
23.d	odd	22	1	inner	460.2.o.a	✓	40
92.h	even	22	1	inner	460.2.o.a	✓	40
115.i	odd	22	1	inner	460.2.o.a	✓	40
460.o	even	22	1	inner	460.2.o.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
460.2.o.a	✓	40	1.a	even	1	1	trivial
460.2.o.a	✓	40	4.b	odd	2	1	inner
460.2.o.a	✓	40	5.b	even	2	1	inner
460.2.o.a	✓	40	20.d	odd	2	1	CM
460.2.o.a	✓	40	23.d	odd	22	1	inner
460.2.o.a	✓	40	92.h	even	22	1	inner
460.2.o.a	✓	40	115.i	odd	22	1	inner
460.2.o.a	✓	40	460.o	even	22	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^40 + 4*T3^38 + 12*T3^36 + 164*T3^34 + 17240*T3^32 + 78732*T3^30 + 426742*T3^28 + 17348068*T3^26 + 223427550*T3^24 + 936486512*T3^22 - 498188482*T3^20 - 4541966992*T3^18 + 141857631105*T3^16 - 43778899232*T3^14 + 8092566769135*T3^12 - 8537034326640*T3^10 + 29420297213231*T3^8 + 19046883937208*T3^6 + 5108426689386*T3^4 + 994162360456*T3^2 + 123657019201