Newform orbit 276.2.k.a

• Label: 276.2.k.a
• Level: $276$
• Weight: $2$
• Character orbit: 276.k
• Analytic conductor: $2.204$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.20387109579\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(8\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1		0		−1.56788	−	0.736032i		0		0.185142	−	1.28769i		0		−4.35485	+	1.98879i		0		1.91651	+	2.30802i		0
5.2		0		−1.25009	+	1.19887i		0		−0.395237	+	2.74894i		0		0.714786	−	0.326432i		0		0.125437	−	2.99738i		0
5.3		0		−1.09629	−	1.34095i		0		−0.333236	+	2.31771i		0		2.57171	−	1.17446i		0		−0.596294	+	2.94014i		0
5.4		0		−1.00876	+	1.40798i		0		0.395237	−	2.74894i		0		0.714786	−	0.326432i		0		−0.964814	−	2.84062i		0
5.5		0		0.297274	−	1.70635i		0		0.377490	−	2.62550i		0		1.06836	−	0.487902i		0		−2.82326	−	1.01451i		0
5.6		0		0.951673	+	1.44718i		0		−0.185142	+	1.28769i		0		−4.35485	+	1.98879i		0		−1.18864	+	2.75448i		0
5.7		0		1.48332	+	0.894295i		0		0.333236	−	2.31771i		0		2.57171	−	1.17446i		0		1.40047	+	2.65305i		0
5.8		0		1.64667	−	0.537087i		0		−0.377490	+	2.62550i		0		1.06836	−	0.487902i		0		2.42308	−	1.76881i		0
17.1		0		−1.72769	+	0.122800i		0		1.67238	−	1.07478i		0		−0.700880	−	0.100771i		0		2.96984	−	0.424320i		0
17.2		0		−1.38704	−	1.03737i		0		−1.67238	+	1.07478i		0		−0.700880	−	0.100771i		0		0.847741	+	2.87773i		0
17.3		0		−1.27466	+	1.17271i		0		−2.95319	+	1.89790i		0		0.486747	+	0.0699836i		0		0.249516	−	2.98961i		0
17.4		0		−0.438299	−	1.67568i		0		2.95319	−	1.89790i		0		0.486747	+	0.0699836i		0		−2.61579	+	1.46889i		0
17.5		0		0.604048	+	1.62331i		0		0.998768	−	0.641869i		0		3.17327	+	0.456247i		0		−2.27025	+	1.96111i		0
17.6		0		1.38367	+	1.04185i		0		−2.86447	+	1.84088i		0		−2.95914	−	0.425460i		0		0.829091	+	2.88316i		0
17.7		0		1.38578	−	1.03904i		0		−0.998768	+	0.641869i		0		3.17327	+	0.456247i		0		0.840791	−	2.87977i		0
17.8		0		1.72729	−	0.128392i		0		2.86447	−	1.84088i		0		−2.95914	−	0.425460i		0		2.96703	−	0.443540i		0
53.1		0		−1.73158	+	0.0405044i		0		−0.551710	−	1.20808i		0		0.335628	+	1.14304i		0		2.99672	−	0.140273i		0
53.2		0		−1.67064	−	0.457117i		0		1.12657	+	2.46685i		0		−1.33973	−	4.56271i		0		2.58209	+	1.52736i		0
53.3		0		−0.756167	+	1.55827i		0		0.551710	+	1.20808i		0		0.335628	+	1.14304i		0		−1.85642	−	2.35663i		0
53.4		0		−0.751560	−	1.56050i		0		1.12484	+	2.46306i		0		1.26778	+	4.31765i		0		−1.87032	+	2.34562i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
23.d	odd	22	1	inner
69.g	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	276.2.k.a	✓	80
3.b	odd	2	1	inner	276.2.k.a	✓	80
23.d	odd	22	1	inner	276.2.k.a	✓	80
69.g	even	22	1	inner	276.2.k.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.2.k.a	✓	80	1.a	even	1	1	trivial
276.2.k.a	✓	80	3.b	odd	2	1	inner
276.2.k.a	✓	80	23.d	odd	22	1	inner
276.2.k.a	✓	80	69.g	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(276, [\chi])\).