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Properties

Label 2033.4.a.a
Level $2033$
Weight $4$
Character orbit 2033.a
Self dual yes
Analytic conductor $119.951$
Analytic rank $1$
Dimension $115$
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] = [2033,4,Mod(1,2033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2033, 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("2033.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2033 = 19 \cdot 107 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2033.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: \(119.950883042\)
Analytic rank: \(1\)
Dimension: \(115\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 115 q - 10 q^{2} - 10 q^{3} + 428 q^{4} - 29 q^{5} - 33 q^{6} - 258 q^{7} - 90 q^{8} + 945 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 115 q - 10 q^{2} - 10 q^{3} + 428 q^{4} - 29 q^{5} - 33 q^{6} - 258 q^{7} - 90 q^{8} + 945 q^{9} - 42 q^{10} - 192 q^{11} + 55 q^{12} - 108 q^{13} - 80 q^{14} - 518 q^{15} + 1420 q^{16} - 208 q^{17} - 563 q^{18} - 2185 q^{19} - 340 q^{20} - 122 q^{21} - 532 q^{22} - 611 q^{23} - 491 q^{24} + 2132 q^{25} - 465 q^{26} - 526 q^{27} - 1598 q^{28} - 606 q^{29} - 2002 q^{30} - 770 q^{31} - 1645 q^{32} + 12 q^{33} - 1581 q^{34} - 1084 q^{35} + 285 q^{36} - 986 q^{37} + 190 q^{38} - 2424 q^{39} - 2674 q^{40} - 1305 q^{41} - 1903 q^{42} - 3175 q^{43} - 3692 q^{44} - 947 q^{45} - 737 q^{46} - 2517 q^{47} - 123 q^{48} + 4643 q^{49} + 588 q^{50} - 2472 q^{51} - 1317 q^{52} - 872 q^{53} - 3409 q^{54} - 3774 q^{55} - 1904 q^{56} + 190 q^{57} - 3135 q^{58} - 1627 q^{59} - 4002 q^{60} - 3538 q^{61} - 2030 q^{62} - 6964 q^{63} + 3902 q^{64} - 302 q^{65} + 30 q^{66} - 5015 q^{67} - 2270 q^{68} + 590 q^{69} - 5802 q^{70} - 1762 q^{71} - 7539 q^{72} - 5014 q^{73} - 3076 q^{74} - 3254 q^{75} - 8132 q^{76} - 898 q^{77} - 3533 q^{78} - 8647 q^{79} - 1777 q^{80} + 5155 q^{81} - 5584 q^{82} - 4746 q^{83} - 4959 q^{84} - 4874 q^{85} - 4546 q^{86} - 4582 q^{87} - 7234 q^{88} - 1669 q^{89} + 505 q^{90} - 1904 q^{91} - 4554 q^{92} - 5312 q^{93} - 5232 q^{94} + 551 q^{95} - 11516 q^{96} - 4820 q^{97} - 5628 q^{98} - 8338 q^{99}+O(q^{100}) \) 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 −5.52462 9.15880 22.5214 9.66139 −50.5989 5.77736 −80.2252 56.8837 −53.3755
1.2 −5.44937 −7.18480 21.6956 −4.47751 39.1526 −24.5226 −74.6322 24.6214 24.3996
1.3 −5.40530 5.29943 21.2173 14.5599 −28.6450 −30.2183 −71.4436 1.08391 −78.7009
1.4 −5.35410 3.12958 20.6664 −5.77633 −16.7561 −34.0554 −67.8174 −17.2057 30.9271
1.5 −5.24082 −0.570770 19.4662 −6.36329 2.99130 4.71243 −60.0920 −26.6742 33.3488
1.6 −5.23563 7.27741 19.4118 −9.66438 −38.1019 −9.43377 −59.7482 25.9608 50.5991
1.7 −5.18885 −6.33588 18.9242 −12.7172 32.8760 7.65481 −56.6841 13.1434 65.9877
1.8 −5.18863 −3.61623 18.9218 15.0162 18.7633 8.65084 −56.6694 −13.9229 −77.9136
1.9 −5.17374 4.01661 18.7676 −6.40925 −20.7809 28.5056 −55.7088 −10.8669 33.1598
1.10 −4.91164 −8.86196 16.1243 11.6285 43.5268 −11.5963 −39.9034 51.5343 −57.1150
1.11 −4.76172 −0.839810 14.6740 5.91700 3.99894 27.6871 −31.7798 −26.2947 −28.1751
1.12 −4.69631 −5.76488 14.0553 17.8104 27.0737 15.2202 −28.4375 6.23388 −83.6432
1.13 −4.69026 −6.98403 13.9985 −4.58929 32.7569 23.1992 −28.1347 21.7767 21.5250
1.14 −4.48548 −0.874596 12.1195 3.23997 3.92298 −34.0134 −18.4781 −26.2351 −14.5328
1.15 −4.42128 7.07174 11.5477 −16.3175 −31.2661 4.06075 −15.6852 23.0094 72.1440
1.16 −4.40596 3.02565 11.4125 7.85777 −13.3309 −10.7453 −15.0352 −17.8454 −34.6210
1.17 −4.29990 −2.15134 10.4891 −13.9840 9.25055 1.06182 −10.7030 −22.3717 60.1300
1.18 −4.29450 6.91009 10.4427 7.70152 −29.6754 20.9033 −10.4904 20.7493 −33.0742
1.19 −4.16525 −2.64667 9.34927 −12.8060 11.0240 −28.3353 −5.62002 −19.9951 53.3401
1.20 −4.15770 −3.29240 9.28647 16.8339 13.6888 5.95488 −5.34877 −16.1601 −69.9904
See next 80 embeddings (of 115 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.115
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \( +1 \)
\(107\) \( -1 \)

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 2033.4.a.a ✓ 115
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2033.4.a.a ✓ 115 1.a even 1 1 trivial