Properties

Label 1441.2.a.e
Level $1441$
Weight $2$
Character orbit 1441.a
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $28$
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: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28q + 7q^{2} - 2q^{3} + 27q^{4} + 3q^{5} - q^{6} + 7q^{7} + 21q^{8} + 28q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q + 7q^{2} - 2q^{3} + 27q^{4} + 3q^{5} - q^{6} + 7q^{7} + 21q^{8} + 28q^{9} + 14q^{10} + 28q^{11} - 6q^{12} + 3q^{13} - q^{14} + 19q^{15} + 29q^{16} + 9q^{17} - 2q^{18} + 20q^{19} + 6q^{20} + 6q^{21} + 7q^{22} + 24q^{23} + 20q^{24} + 23q^{25} + 10q^{26} - 20q^{27} - 3q^{28} + 43q^{29} + 11q^{30} + 3q^{31} + 44q^{32} - 2q^{33} - 28q^{34} + 32q^{35} + 24q^{36} - 4q^{37} + 24q^{38} + 37q^{39} + 22q^{40} + 32q^{41} - 27q^{42} + 25q^{43} + 27q^{44} - 36q^{45} + 10q^{46} + 19q^{47} + 42q^{48} + 17q^{49} + q^{50} + 39q^{51} - 19q^{52} + 5q^{53} + 6q^{54} + 3q^{55} + 8q^{56} + 2q^{57} + 21q^{58} + 44q^{59} + 65q^{60} + 28q^{61} + 60q^{62} - 8q^{63} + 5q^{64} + 33q^{65} - q^{66} + 7q^{67} + 13q^{68} - 22q^{69} + 9q^{70} + 117q^{71} - 17q^{72} + 7q^{73} + 41q^{74} - 40q^{75} + 34q^{76} + 7q^{77} - 97q^{78} + 48q^{79} + 41q^{80} + 40q^{81} + 2q^{82} + 22q^{83} + 27q^{84} + 30q^{85} + 24q^{86} + 37q^{87} + 21q^{88} - 6q^{89} + 4q^{90} - 33q^{91} + 18q^{92} + 5q^{93} - 43q^{94} + 64q^{95} + 55q^{96} - 50q^{97} + 97q^{98} + 28q^{99} + O(q^{100}) \)

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 −2.46758 −2.74867 4.08895 0.488919 6.78255 −1.50214 −5.15465 4.55516 −1.20645
1.2 −2.36893 0.351154 3.61185 −1.64180 −0.831861 −1.35814 −3.81837 −2.87669 3.88932
1.3 −2.33619 2.29063 3.45776 −0.314509 −5.35135 0.543204 −3.40560 2.24701 0.734752
1.4 −2.09032 1.02488 2.36944 3.67569 −2.14232 2.35755 −0.772245 −1.94963 −7.68337
1.5 −1.79989 −0.0643329 1.23961 −3.25644 0.115792 2.45508 1.36862 −2.99586 5.86125
1.6 −1.77267 −3.40600 1.14234 −3.60328 6.03770 0.417068 1.52034 8.60085 6.38741
1.7 −1.13972 3.40925 −0.701031 −0.104086 −3.88560 1.00506 3.07843 8.62297 0.118629
1.8 −1.03351 −2.03030 −0.931861 −0.515805 2.09833 −3.45818 3.03010 1.12211 0.533089
1.9 −1.01237 −1.33231 −0.975116 3.44940 1.34878 1.50282 3.01190 −1.22496 −3.49205
1.10 −0.660505 2.12062 −1.56373 2.37769 −1.40068 3.00733 2.35386 1.49703 −1.57048
1.11 −0.574950 1.45629 −1.66943 −2.31674 −0.837294 −3.08132 2.10974 −0.879222 1.33201
1.12 −0.452030 −0.254542 −1.79567 −0.679800 0.115061 3.95437 1.71576 −2.93521 0.307290
1.13 0.00299522 0.0189616 −1.99999 1.18959 5.67941e−5 0 −5.08173 −0.0119809 −2.99964 0.00356309
1.14 0.235116 −2.49285 −1.94472 2.71737 −0.586108 3.95783 −0.927465 3.21431 0.638897
1.15 0.544027 2.32406 −1.70404 −4.20016 1.26435 −0.904548 −2.01509 2.40124 −2.28500
1.16 0.635564 −1.42688 −1.59606 2.67263 −0.906871 −2.11184 −2.28553 −0.964025 1.69862
1.17 0.851882 2.55735 −1.27430 2.24117 2.17856 −0.305679 −2.78931 3.54005 1.90921
1.18 1.06795 −2.13569 −0.859479 −3.41004 −2.28082 1.64444 −3.05379 1.56119 −3.64175
1.19 1.13327 0.404748 −0.715692 −1.18320 0.458690 4.77646 −3.07762 −2.83618 −1.34089
1.20 1.67300 −1.49184 0.798939 −1.12664 −2.49585 −0.438386 −2.00938 −0.774411 −1.88488
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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.e 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1441.2.a.e 28 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{28} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1441))\).