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Properties

Label 1441.4.a.c
Level $1441$
Weight $4$
Character orbit 1441.a
Self dual yes
Analytic conductor $85.022$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1441,4,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1441.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(85.0217523183\)
Analytic rank: \(0\)
Dimension: \(84\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.59207 2.65702 23.2713 12.4964 −14.8583 −8.00528 −85.3980 −19.9402 −69.8810
1.2 −5.44368 2.05433 21.6337 3.77556 −11.1831 −23.4172 −74.2175 −22.7797 −20.5530
1.3 −5.25317 −10.3044 19.5957 −18.0312 54.1305 −26.5546 −60.9144 79.1798 94.7210
1.4 −5.22169 9.75811 19.2660 5.85487 −50.9538 21.2557 −58.8275 68.2208 −30.5723
1.5 −5.13763 0.841813 18.3952 −3.56882 −4.32492 24.0012 −53.4067 −26.2914 18.3352
1.6 −4.95141 7.86168 16.5165 22.2161 −38.9264 −21.9144 −42.1686 34.8060 −110.001
1.7 −4.94944 −0.986242 16.4970 −9.10214 4.88135 −0.117691 −42.0552 −26.0273 45.0505
1.8 −4.94545 −7.30968 16.4575 −2.24027 36.1497 −13.8801 −41.8261 26.4315 11.0791
1.9 −4.86629 8.51563 15.6808 −14.8824 −41.4395 −8.95651 −37.3770 45.5159 72.4219
1.10 −4.62908 −6.73541 13.4284 −11.7563 31.1787 27.0401 −25.1283 18.3657 54.4209
1.11 −4.51063 −9.84938 12.3457 17.1795 44.4268 17.4942 −19.6020 70.0102 −77.4904
1.12 −4.49484 −4.17061 12.2036 2.72170 18.7463 3.24249 −18.8947 −9.60598 −12.2336
1.13 −4.12900 4.44152 9.04867 −7.53551 −18.3391 −5.95864 −4.32996 −7.27286 31.1142
1.14 −3.93057 5.24516 7.44938 13.0980 −20.6165 29.5585 2.16424 0.511720 −51.4825
1.15 −3.91972 −6.88382 7.36419 10.4958 26.9826 12.1414 2.49219 20.3870 −41.1406
1.16 −3.89777 0.451407 7.19260 9.64232 −1.75948 −28.6536 3.14706 −26.7962 −37.5835
1.17 −3.58764 1.94345 4.87115 5.55932 −6.97238 7.62393 11.2252 −23.2230 −19.9448
1.18 −3.57727 6.26190 4.79686 −11.2090 −22.4005 −24.1930 11.4585 12.2114 40.0975
1.19 −3.52442 −4.70924 4.42151 7.44138 16.5973 32.1322 12.6121 −4.82309 −26.2265
1.20 −3.46488 4.89335 4.00542 −17.5510 −16.9549 8.47973 13.8407 −3.05509 60.8121
See all 84 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.84
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 1441.4.a.c ✓ 84
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1441.4.a.c ✓ 84 1.a even 1 1 trivial