Properties

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 $1$

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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.

\(\operatorname{Tr}(f)(q) = \) \( 23q - 7q^{2} - 3q^{3} + 15q^{4} - 9q^{5} - 11q^{6} - 12q^{7} - 21q^{8} + 12q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 23q - 7q^{2} - 3q^{3} + 15q^{4} - 9q^{5} - 11q^{6} - 12q^{7} - 21q^{8} + 12q^{9} - 2q^{10} + 23q^{11} + 8q^{12} - 24q^{13} - 13q^{14} - 27q^{15} + 7q^{16} - 7q^{17} - 14q^{18} - 18q^{19} - 4q^{20} - 29q^{21} - 7q^{22} - 26q^{23} - 4q^{24} + 18q^{25} + 8q^{26} - 3q^{27} - 11q^{28} - 45q^{29} + 19q^{30} - 23q^{31} - 34q^{32} - 3q^{33} - 2q^{34} - 18q^{35} - 6q^{36} - 2q^{37} - 8q^{38} - 40q^{39} - 24q^{40} - 23q^{41} + 59q^{42} - 14q^{43} + 15q^{44} - 18q^{45} - 12q^{46} - 55q^{47} + 10q^{48} + 11q^{49} - 41q^{50} - 21q^{51} - 37q^{52} - 10q^{53} - 68q^{54} - 9q^{55} + 2q^{56} - 18q^{57} + 27q^{58} - 75q^{59} - 63q^{60} - 55q^{61} + 14q^{62} - 16q^{63} + 19q^{64} - 25q^{65} - 11q^{66} + 17q^{67} + 41q^{68} - 22q^{69} + 27q^{70} - 105q^{71} - 11q^{72} - 3q^{73} - 39q^{74} + 25q^{75} - 30q^{76} - 12q^{77} + 25q^{78} - 48q^{79} - 37q^{80} + 3q^{81} + 36q^{82} + 4q^{83} - 111q^{84} - 30q^{85} + 22q^{86} + 5q^{87} - 21q^{88} - 39q^{89} + 100q^{90} - 22q^{91} - 30q^{92} - 5q^{93} + 11q^{94} - 88q^{95} + 13q^{96} + 24q^{97} - 91q^{98} + 12q^{99} + O(q^{100}) \)

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
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

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 \(T_{2}^{23} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1441))\).