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Properties

Label 935.2.u.f
Level $935$
Weight $2$
Character orbit 935.u
Analytic conductor $7.466$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [935,2,Mod(86,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.86");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.u (of order \(5\), degree \(4\), minimal)

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: no
Analytic conductor: \(7.46601258899\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(15\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + q^{2} - 6 q^{3} - 11 q^{4} + 15 q^{5} + 12 q^{6} + 6 q^{7} - 16 q^{8} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q + q^{2} - 6 q^{3} - 11 q^{4} + 15 q^{5} + 12 q^{6} + 6 q^{7} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 3 q^{11} + 52 q^{12} + 5 q^{13} - 3 q^{14} + 6 q^{15} - 13 q^{16} - 15 q^{17} + 7 q^{18} - 12 q^{19} + 16 q^{20} + 32 q^{21} + 34 q^{22} + 30 q^{23} + 19 q^{24} - 15 q^{25} - 30 q^{26} - 42 q^{27} + 23 q^{28} + 13 q^{29} + 8 q^{30} - 4 q^{31} + 34 q^{32} + 14 q^{33} + 6 q^{34} - q^{35} - 57 q^{36} - 40 q^{37} - 53 q^{38} + 14 q^{39} + 16 q^{40} - 16 q^{41} - 21 q^{42} + 64 q^{43} + 6 q^{44} - 60 q^{45} - 39 q^{46} - 19 q^{47} - 136 q^{48} - 65 q^{49} + q^{50} - 6 q^{51} - 52 q^{52} - 97 q^{53} + 26 q^{54} - 3 q^{55} + 36 q^{56} + 36 q^{57} - 48 q^{58} - 23 q^{59} - 27 q^{60} + 46 q^{61} + 77 q^{62} - 18 q^{63} - 16 q^{64} - 10 q^{65} + 10 q^{66} + 112 q^{67} - 16 q^{68} - 23 q^{69} + 3 q^{70} - 36 q^{71} + 90 q^{72} + 41 q^{73} - 70 q^{74} - 6 q^{75} + 76 q^{76} + 13 q^{77} + 122 q^{78} - 46 q^{79} + 8 q^{80} - 143 q^{81} - 156 q^{82} + 130 q^{84} + 15 q^{85} - 70 q^{86} + 66 q^{87} - 16 q^{88} + 76 q^{89} + 8 q^{90} - 13 q^{91} + 11 q^{92} - 49 q^{93} + 33 q^{94} + 12 q^{95} - 21 q^{96} - 66 q^{97} + 84 q^{98} + 49 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
86.1 −0.800707 + 2.46432i −2.34948 + 1.70700i −3.81372 − 2.77083i −0.309017 − 0.951057i −2.32535 − 7.15670i 0.944553 + 0.686258i 5.68935 − 4.13355i 1.67917 − 5.16797i 2.59114
86.2 −0.614839 + 1.89228i 0.868182 − 0.630771i −1.58466 − 1.15132i −0.309017 − 0.951057i 0.659803 + 2.03067i −0.627595 − 0.455974i −0.0664036 + 0.0482450i −0.571183 + 1.75792i 1.98966
86.3 −0.504148 + 1.55161i −0.0732046 + 0.0531863i −0.535291 − 0.388912i −0.309017 − 0.951057i −0.0456183 − 0.140399i 3.25502 + 2.36491i −1.76645 + 1.28340i −0.924521 + 2.84538i 1.63146
86.4 −0.477239 + 1.46879i −1.72684 + 1.25462i −0.311551 − 0.226355i −0.309017 − 0.951057i −1.01866 − 3.13512i −0.764516 − 0.555454i −2.01770 + 1.46595i 0.480851 − 1.47991i 1.54438
86.5 −0.309845 + 0.953604i 2.41998 − 1.75822i 0.804677 + 0.584632i −0.309017 − 0.951057i 0.926825 + 2.85248i 2.00771 + 1.45868i −2.42920 + 1.76492i 1.83792 − 5.65652i 1.00268
86.6 −0.230848 + 0.710479i 0.396082 − 0.287770i 1.16655 + 0.847545i −0.309017 − 0.951057i 0.113020 + 0.347839i −0.145072 − 0.105401i −2.08020 + 1.51135i −0.852982 + 2.62521i 0.747041
86.7 −0.0273903 + 0.0842987i −0.961229 + 0.698373i 1.61168 + 1.17095i −0.309017 − 0.951057i −0.0325436 − 0.100159i −1.94256 − 1.41135i −0.286272 + 0.207989i −0.490816 + 1.51058i 0.0886369
86.8 0.00391365 − 0.0120450i −2.73025 + 1.98364i 1.61790 + 1.17548i −0.309017 − 0.951057i 0.0132077 + 0.0406491i −2.81420 − 2.04464i 0.0409826 − 0.0297756i 2.59237 − 7.97849i −0.0126648
86.9 0.130914 − 0.402910i 0.648983 − 0.471514i 1.47284 + 1.07008i −0.309017 − 0.951057i −0.105017 − 0.323210i 0.497409 + 0.361389i 1.30943 − 0.951358i −0.728197 + 2.24116i −0.423645
86.10 0.326187 − 1.00390i 2.29188 − 1.66515i 0.716618 + 0.520653i −0.309017 − 0.951057i −0.924059 − 2.84396i 1.98065 + 1.43903i 2.46437 − 1.79047i 1.55294 − 4.77944i −1.05556
86.11 0.472918 − 1.45549i −0.557471 + 0.405027i −0.276771 − 0.201086i −0.309017 − 0.951057i 0.325875 + 1.00294i 1.98570 + 1.44269i 2.05266 − 1.49135i −0.780323 + 2.40159i −1.53039
86.12 0.591996 − 1.82198i 1.18559 − 0.861385i −1.35110 − 0.981633i −0.309017 − 0.951057i −0.867555 − 2.67006i −1.89449 − 1.37642i 0.511371 − 0.371533i −0.263401 + 0.810664i −1.91574
86.13 0.654246 − 2.01356i −0.811613 + 0.589672i −2.00836 − 1.45916i −0.309017 − 0.951057i 0.656346 + 2.02002i 2.82302 + 2.05104i −0.826390 + 0.600408i −0.616047 + 1.89600i −2.11718
86.14 0.789956 − 2.43123i −2.62219 + 1.90513i −3.66883 − 2.66556i −0.309017 − 0.951057i 2.56041 + 7.88013i 1.17572 + 0.854212i −5.24256 + 3.80895i 2.31930 − 7.13808i −2.55635
86.15 0.803904 − 2.47416i −0.832515 + 0.604858i −3.85719 − 2.80241i −0.309017 − 0.951057i 0.827254 + 2.54602i −2.74528 − 1.99456i −5.82513 + 4.23220i −0.599822 + 1.84606i −2.60149
256.1 −2.12200 + 1.54173i 0.131749 + 0.405483i 1.50794 − 4.64098i 0.809017 + 0.587785i −0.904717 − 0.657315i −0.371168 + 1.14234i 2.33418 + 7.18388i 2.27999 − 1.65651i −2.62294
256.2 −2.04260 + 1.48404i −0.387880 − 1.19377i 1.35182 − 4.16049i 0.809017 + 0.587785i 2.56389 + 1.86277i 0.926236 − 2.85066i 1.85267 + 5.70193i 1.15241 − 0.837276i −2.52480
256.3 −1.68323 + 1.22294i −0.499388 − 1.53696i 0.719645 − 2.21484i 0.809017 + 0.587785i 2.72018 + 1.97633i −1.26719 + 3.90000i 0.211411 + 0.650656i 0.314199 − 0.228279i −2.08058
256.4 −1.16040 + 0.843081i 1.01641 + 3.12819i 0.0177114 − 0.0545101i 0.809017 + 0.587785i −3.81676 − 2.77304i −1.04870 + 3.22756i −0.861063 − 2.65008i −6.32545 + 4.59571i −1.43433
256.5 −1.09048 + 0.792281i 0.746244 + 2.29670i −0.0565944 + 0.174180i 0.809017 + 0.587785i −2.63340 − 1.91328i 1.58377 − 4.87435i −0.909337 − 2.79865i −2.29091 + 1.66445i −1.34791
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 86.15
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.u.f ✓ 60
11.c even 5 1 inner 935.2.u.f ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.u.f ✓ 60 1.a even 1 1 trivial
935.2.u.f ✓ 60 11.c even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{60} - T_{2}^{59} + 21 T_{2}^{58} - 10 T_{2}^{57} + 267 T_{2}^{56} - 116 T_{2}^{55} + 2870 T_{2}^{54} + \cdots + 25 \) acting on \(S_{2}^{\mathrm{new}}(935, [\chi])\). Copy content Toggle raw display