Newform orbit 1441.2.a.c

• Label: 1441.2.a.c
• Level: $1441$
• Weight: $2$
• Character orbit: 1441.a
• Self dual: yes
• Analytic conductor: $11.506$
• Analytic rank: $1$
• Dimension: $23$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.5064429313\)
Analytic rank:	\(1\)
Dimension:	\(23\)
Twist minimal:	yes
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.78830			−0.518611			5.77463			−0.346547			1.44605			3.25187			−10.5248			−2.73104			0.966278
1.2	−2.56442			0.292938			4.57625			3.66360			−0.751215			−5.05392			−6.60659			−2.91419			−9.39502
1.3	−2.50019			3.16294			4.25093			−4.26480			−7.90794			−1.67608			−5.62776			7.00418			10.6628
1.4	−2.24881			−1.99348			3.05713			−0.623302			4.48295			4.70119			−2.37729			0.973955			1.40169
1.5	−1.84752			2.72852			1.41334			1.47029			−5.04100			−2.80791			1.08387			4.44483			−2.71640
1.6	−1.75710			−2.59102			1.08739			2.84782			4.55267			2.84815			1.60354			3.71338			−5.00390
1.7	−1.59929			1.84862			0.557714			−2.20532			−2.95647			0.234218			2.30663			0.417399			3.52693
1.8	−1.52508			−0.420875			0.325868			−3.40099			0.641868			−3.60038			2.55318			−2.82286			5.18678
1.9	−1.24808			−0.917360			−0.442292			1.92098			1.14494			0.0608487			3.04818			−2.15845			−2.39755
1.10	−1.00403			1.28366			−0.991926			0.810675			−1.28883			−2.46332			3.00398			−1.35222			−0.813941
1.11	−0.363851			−2.50967			−1.86761			−1.53260			0.913144			−1.87155			1.40723			3.29843			0.557639
1.12	−0.288878			2.13203			−1.91655			−3.62334			−0.615896			3.72928			1.13141			1.54555			1.04670
1.13	−0.169669			−1.85024			−1.97121			−3.73136			0.313927			1.69497			0.673790			0.423370			0.633095
1.14	0.338964			0.415229			−1.88510			2.48639			0.140748			1.37068			−1.31691			−2.82758			0.842796
1.15	0.495822			−0.133739			−1.75416			−0.493567			−0.0663105			1.67893			−1.86140			−2.98211			−0.244721
1.16	0.665447			−3.11635			−1.55718			−0.365961			−2.07377			−1.41982			−2.36711			6.71165			−0.243528
1.17	0.714474			2.60520			−1.48953			−0.266226			1.86135			−4.25119			−2.49318			3.78706			−0.190211
1.18	1.32496			0.816970			−0.244480			−1.13056			1.08245			0.353069			−2.97385			−2.33256			−1.49794
1.19	1.34408			−2.56743			−0.193462			4.05031			−3.45081			−3.27147			−2.94818			3.59168			5.44393
1.20	1.75422			−0.900924			1.07730			1.37756			−1.58042			−1.58298			−1.61862			−2.18834			2.41656

Atkin-Lehner signs

\( p \)	Sign
\(11\)	\(-1\)
\(131\)	\(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1441.2.a.c	✓	23

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1441.2.a.c	✓	23	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^23 + 7*T2^22 - 6*T2^21 - 140*T2^20 - 138*T2^19 + 1131*T2^18 + 2001*T2^17 - 4693*T2^16 - 11448*T2^15 + 10339*T2^14 + 35570*T2^13 - 10374*T2^12 - 64708*T2^11 - 415*T2^10 + 69507*T2^9 + 9658*T2^8 - 42801*T2^7 - 7047*T2^6 + 14101*T2^5 + 1918*T2^4 - 2061*T2^3 - 279*T2^2 + 104*T2 + 16