Properties

Label 1441.2.a.d
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.

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.66894 0.662508 5.12325 −2.84363 −1.76820 −0.180196 −8.33576 −2.56108 7.58947
1.2 −2.52155 −0.648204 4.35820 2.39834 1.63448 −0.583352 −5.94631 −2.57983 −6.04753
1.3 −2.47542 2.04682 4.12769 −2.23639 −5.06674 4.08338 −5.26693 1.18947 5.53600
1.4 −2.16219 −2.96733 2.67508 2.79492 6.41593 0.0561777 −1.45964 5.80503 −6.04316
1.5 −2.10794 1.73442 2.44341 0.240614 −3.65606 0.0249073 −0.934681 0.00822254 −0.507199
1.6 −2.06686 −1.75987 2.27189 −3.28939 3.63739 1.71043 −0.561957 0.0971338 6.79870
1.7 −1.61515 −2.31019 0.608714 −1.59855 3.73131 −4.36629 2.24714 2.33698 2.58190
1.8 −1.47853 1.20449 0.186052 1.76198 −1.78087 −2.63188 2.68198 −1.54921 −2.60515
1.9 −1.26006 0.450963 −0.412243 1.25945 −0.568242 3.91553 3.03958 −2.79663 −1.58699
1.10 −0.850138 −0.411295 −1.27727 −3.81435 0.349658 2.53746 2.78613 −2.83084 3.24272
1.11 −0.793163 2.98559 −1.37089 −2.40573 −2.36806 −3.11236 2.67367 5.91372 1.90814
1.12 −0.265643 −2.11945 −1.92943 2.15570 0.563016 −4.44888 1.04383 1.49206 −0.572646
1.13 −0.248714 −2.31541 −1.93814 3.78233 0.575874 0.228936 0.979470 2.36112 −0.940718
1.14 −0.200388 2.28550 −1.95984 −0.516505 −0.457986 −2.27895 0.793506 2.22349 0.103502
1.15 0.465389 1.44715 −1.78341 0.0108050 0.673486 0.934440 −1.76076 −0.905766 0.00502854
1.16 0.947276 −2.80681 −1.10267 −2.22661 −2.65882 3.55035 −2.93908 4.87818 −2.10922
1.17 1.04685 0.462154 −0.904108 2.89071 0.483806 −3.03594 −3.04016 −2.78641 3.02614
1.18 1.39370 1.35746 −0.0576006 −3.24463 1.89189 2.34571 −2.86768 −1.15730 −4.52204
1.19 1.54502 2.73368 0.387096 −3.25406 4.22360 −3.29481 −2.49197 4.47303 −5.02759
1.20 1.83773 −0.0182258 1.37726 1.49121 −0.0334942 −3.57754 −1.14443 −2.99967 2.74044
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
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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.d 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1441.2.a.d 23 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{23} + 7 T_{2}^{22} - 8 T_{2}^{21} - 156 T_{2}^{20} - 142 T_{2}^{19} + 1401 T_{2}^{18} + 2517 T_{2}^{17} - 6381 T_{2}^{16} - 16668 T_{2}^{15} + 14473 T_{2}^{14} + 59682 T_{2}^{13} - 8398 T_{2}^{12} - 124704 T_{2}^{11} + \cdots - 76 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1441))\). Copy content Toggle raw display