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Properties

Label 2491.4.a.d
Level $2491$
Weight $4$
Character orbit 2491.a
Self dual yes
Analytic conductor $146.974$
Analytic rank $0$
Dimension $157$
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] = [2491,4,Mod(1,2491)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2491, 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("2491.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2491 = 47 \cdot 53 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2491.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: \(146.973757824\)
Analytic rank: \(0\)
Dimension: \(157\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 157 q + 30 q^{2} + 32 q^{3} + 676 q^{4} + 125 q^{5} + 80 q^{6} + 102 q^{7} + 360 q^{8} + 1671 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 157 q + 30 q^{2} + 32 q^{3} + 676 q^{4} + 125 q^{5} + 80 q^{6} + 102 q^{7} + 360 q^{8} + 1671 q^{9} + 70 q^{10} + 305 q^{11} + 312 q^{12} + 174 q^{13} + 193 q^{14} + 144 q^{15} + 3116 q^{16} + 333 q^{17} + 1017 q^{18} + 450 q^{19} + 80 q^{20} + 1488 q^{21} + 414 q^{22} + 399 q^{23} + 953 q^{24} + 4588 q^{25} + 700 q^{26} + 662 q^{27} + 813 q^{28} + 2264 q^{29} + 274 q^{30} + 655 q^{31} + 2785 q^{32} + 842 q^{33} + 475 q^{34} + 1804 q^{35} + 8708 q^{36} + 998 q^{37} + 500 q^{38} + 1274 q^{39} + 758 q^{40} + 2894 q^{41} + 963 q^{42} + 385 q^{43} + 3298 q^{44} + 3531 q^{45} + 1125 q^{46} + 7379 q^{47} + 2602 q^{48} + 9459 q^{49} + 3989 q^{50} + 3192 q^{51} + 1219 q^{52} + 8321 q^{53} + 4031 q^{54} + 1365 q^{55} + 3129 q^{56} + 562 q^{57} + 1782 q^{58} + 2103 q^{59} + 2715 q^{60} + 2740 q^{61} + 2516 q^{62} + 3202 q^{63} + 16182 q^{64} + 1914 q^{65} + 4110 q^{66} + 938 q^{67} + 3203 q^{68} - 512 q^{69} - 2192 q^{70} + 4918 q^{71} + 13121 q^{72} + 5606 q^{73} + 4248 q^{74} + 8304 q^{75} + 6035 q^{76} + 3828 q^{77} - 21 q^{78} + 2951 q^{79} + 3075 q^{80} + 15845 q^{81} - 1120 q^{82} + 7884 q^{83} + 14423 q^{84} + 7387 q^{85} + 8051 q^{86} + 2688 q^{87} + 6728 q^{88} + 4079 q^{89} + 4102 q^{90} + 1234 q^{91} + 4937 q^{92} + 8080 q^{93} + 1410 q^{94} + 2962 q^{95} + 14571 q^{96} + 2411 q^{97} + 11944 q^{98} + 11369 q^{99}+O(q^{100}) \) 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 −5.56108 2.65040 22.9256 0.423205 −14.7391 22.8777 −83.0022 −19.9754 −2.35347
1.2 −5.51513 −7.73097 22.4167 −14.4052 42.6373 −23.9332 −79.5098 32.7679 79.4468
1.3 −5.49142 −9.78694 22.1557 12.7072 53.7442 −14.1571 −77.7348 68.7842 −69.7808
1.4 −5.23403 4.25373 19.3951 21.3904 −22.2642 33.4309 −59.6424 −8.90576 −111.958
1.5 −5.21763 −2.50383 19.2236 −6.84456 13.0641 3.93878 −58.5607 −20.7308 35.7124
1.6 −5.21612 7.38435 19.2079 −12.3571 −38.5177 −19.7715 −58.4618 27.5287 64.4559
1.7 −5.20238 9.01120 19.0648 −1.01309 −46.8797 −20.4401 −57.5633 54.2018 5.27049
1.8 −5.18796 −1.85167 18.9150 4.98463 9.60640 −2.30915 −56.6265 −23.5713 −25.8601
1.9 −5.16821 0.993713 18.7104 15.4357 −5.13572 −5.78519 −55.3537 −26.0125 −79.7748
1.10 −5.10086 3.23728 18.0188 −12.4480 −16.5129 19.5370 −51.1045 −16.5200 63.4958
1.11 −5.10059 −3.20746 18.0160 17.0976 16.3599 11.6853 −51.0874 −16.7122 −87.2076
1.12 −5.08783 −7.04945 17.8860 0.490769 35.8664 5.95960 −50.2981 22.6948 −2.49695
1.13 −5.02638 7.51511 17.2645 3.89434 −37.7738 −13.0810 −46.5669 29.4769 −19.5745
1.14 −4.84721 4.13731 15.4955 −14.0743 −20.0544 −0.273019 −36.3322 −9.88264 68.2213
1.15 −4.65854 −5.56216 13.7020 −7.16741 25.9116 8.04791 −26.5631 3.93760 33.3897
1.16 −4.60223 7.49914 13.1805 12.9260 −34.5127 16.1519 −23.8418 29.2370 −59.4883
1.17 −4.56266 −8.36211 12.8178 0.264182 38.1535 30.9286 −21.9822 42.9249 −1.20537
1.18 −4.49603 3.97459 12.2142 −16.6246 −17.8698 −10.3543 −18.9473 −11.2027 74.7447
1.19 −4.48101 9.42383 12.0794 −6.92785 −42.2283 29.3404 −18.2800 61.8087 31.0438
1.20 −4.45551 −4.00505 11.8515 0.444180 17.8445 −23.5540 −17.1606 −10.9596 −1.97905
See next 80 embeddings (of 157 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.157
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(47\) \( -1 \)
\(53\) \( -1 \)

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 2491.4.a.d ✓ 157
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2491.4.a.d ✓ 157 1.a even 1 1 trivial