Properties

Label 1441.4.a.a
Level $1441$
Weight $4$
Character orbit 1441.a
Self dual yes
Analytic conductor $85.022$
Analytic rank $1$
Dimension $77$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(85.0217523183\)
Analytic rank: \(1\)
Dimension: \(77\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 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 −5.64162 −7.12045 23.8278 12.2922 40.1708 10.9151 −89.2945 23.7008 −69.3477
1.2 −5.40673 −0.868288 21.2327 −21.2610 4.69460 −2.80805 −71.5459 −26.2461 114.953
1.3 −5.33631 −6.68713 20.4762 −7.16207 35.6846 10.7265 −66.5769 17.7177 38.2190
1.4 −5.29699 7.09451 20.0581 −14.8169 −37.5796 −28.7336 −63.8717 23.3321 78.4849
1.5 −5.25982 7.15979 19.6657 −3.23464 −37.6592 13.6207 −61.3597 24.2625 17.0137
1.6 −5.03190 −2.13656 17.3200 17.2575 10.7510 25.2731 −46.8972 −22.4351 −86.8378
1.7 −4.96967 4.89807 16.6976 5.95481 −24.3418 15.7482 −43.2240 −3.00887 −29.5934
1.8 −4.71456 −2.68555 14.2271 −6.70082 12.6612 −31.9614 −29.3581 −19.7878 31.5915
1.9 −4.63574 −1.60774 13.4901 19.3385 7.45306 −5.00186 −25.4508 −24.4152 −89.6483
1.10 −4.59373 3.62650 13.1024 −18.1051 −16.6592 32.3039 −23.4390 −13.8485 83.1700
1.11 −4.50745 −6.76078 12.3171 12.7660 30.4739 −21.9914 −19.4592 18.7082 −57.5420
1.12 −4.48446 −6.75386 12.1104 −4.87147 30.2874 −3.19104 −18.4329 18.6146 21.8459
1.13 −4.43460 −0.0589157 11.6657 6.10695 0.261268 −16.7287 −16.2560 −26.9965 −27.0819
1.14 −4.26168 7.45225 10.1619 9.79132 −31.7591 −16.2075 −9.21354 28.5360 −41.7275
1.15 −4.17420 6.84332 9.42394 8.54373 −28.5654 8.29120 −5.94379 19.8310 −35.6632
1.16 −3.69212 −0.963469 5.63174 −13.7159 3.55724 27.6461 8.74389 −26.0717 50.6405
1.17 −3.64691 9.89090 5.29995 −2.78497 −36.0712 −24.8287 9.84683 70.8299 10.1565
1.18 −3.61438 −9.63502 5.06371 −13.1556 34.8246 22.8825 10.6128 65.8336 47.5492
1.19 −3.45787 1.66598 3.95688 −9.64680 −5.76075 −6.00852 13.9806 −24.2245 33.3574
1.20 −3.02808 7.31750 1.16924 −4.74899 −22.1579 3.39383 20.6841 26.5458 14.3803
See all 77 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.77
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 1441.4.a.a 77
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1441.4.a.a 77 1.a even 1 1 trivial