↑

Properties

Label 931.2.u.b
Level $931$
Weight $2$
Character orbit 931.u
Analytic conductor $7.434$
Analytic rank $0$
Dimension $264$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(134,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.134");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.u (of order \(7\), degree \(6\), 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: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(264\)
Relative dimension: \(44\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 264 q - 3 q^{2} - 47 q^{4} - 4 q^{5} + 8 q^{6} - 5 q^{7} - 9 q^{8} - 42 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 264 q - 3 q^{2} - 47 q^{4} - 4 q^{5} + 8 q^{6} - 5 q^{7} - 9 q^{8} - 42 q^{9} - 4 q^{10} + 5 q^{11} - q^{12} + 17 q^{14} + 2 q^{15} - 61 q^{16} + 16 q^{17} + 6 q^{18} + 264 q^{19} + 6 q^{20} - 24 q^{21} - 6 q^{22} - 9 q^{23} + 2 q^{24} - 82 q^{25} - 46 q^{26} - 15 q^{27} - 6 q^{28} - 4 q^{30} - 8 q^{31} + 44 q^{32} - 50 q^{33} + 32 q^{34} - 35 q^{35} - 37 q^{36} + 25 q^{37} - 3 q^{38} - 48 q^{39} - 2 q^{40} + 14 q^{41} - 59 q^{42} - 12 q^{43} - 34 q^{44} + 32 q^{45} - 40 q^{46} + 14 q^{47} - 88 q^{48} + 43 q^{49} + 208 q^{50} - 72 q^{51} - 64 q^{52} - 13 q^{53} - 82 q^{54} + 11 q^{55} - 96 q^{56} - 10 q^{58} - 22 q^{59} + 276 q^{60} - 52 q^{61} - 62 q^{62} + 117 q^{63} + 23 q^{64} - 6 q^{65} + 6 q^{66} + 20 q^{67} + 248 q^{68} + 127 q^{69} + 51 q^{70} + 21 q^{71} - 131 q^{72} - 17 q^{73} - 114 q^{74} - 44 q^{75} - 47 q^{76} - 48 q^{77} - 136 q^{78} - 98 q^{80} + 82 q^{81} - 74 q^{82} - 61 q^{83} - 196 q^{84} - 90 q^{85} + 21 q^{86} + 16 q^{87} - 94 q^{88} + 3 q^{89} + 249 q^{90} + 12 q^{91} - 185 q^{92} - 71 q^{93} + 143 q^{94} - 4 q^{95} - 138 q^{96} + 8 q^{97} + 83 q^{98} + 106 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
134.1 −0.618670 − 2.71057i −1.36820 − 1.71567i −5.16249 + 2.48613i 1.75669 + 2.20282i −3.80397 + 4.77002i −2.34476 + 1.22561i 6.46574 + 8.10778i −0.403981 + 1.76996i 4.88407 − 6.12443i
134.2 −0.597645 − 2.61845i 0.390247 + 0.489354i −4.69719 + 2.26205i −1.48889 − 1.86701i 1.04812 − 1.31430i 2.62974 + 0.290651i 5.38119 + 6.74780i 0.580388 − 2.54285i −3.99884 + 5.01439i
134.3 −0.564183 − 2.47185i −1.27184 − 1.59484i −3.98979 + 1.92138i −2.18675 − 2.74209i −3.22464 + 4.04357i −0.200592 − 2.63814i 3.83873 + 4.81361i −0.258363 + 1.13196i −5.54432 + 6.95235i
134.4 −0.564015 − 2.47111i 1.49318 + 1.87239i −3.98635 + 1.91972i 0.696263 + 0.873087i 3.78470 − 4.74587i 1.39163 − 2.25019i 3.83154 + 4.80460i −0.608686 + 2.66683i 1.76479 − 2.21298i
134.5 −0.561549 − 2.46031i 1.09950 + 1.37873i −3.93583 + 1.89540i 2.33444 + 2.92729i 2.77467 − 3.47933i 0.993558 + 2.45211i 3.72657 + 4.67297i −0.0244315 + 0.107041i 5.89113 − 7.38724i
134.6 −0.489110 − 2.14293i −0.609174 − 0.763880i −2.55098 + 1.22849i 1.32140 + 1.65698i −1.33899 + 1.67904i −2.08594 − 1.62753i 1.13937 + 1.42872i 0.455143 − 1.99411i 2.90448 − 3.64210i
134.7 −0.486332 − 2.13076i 1.84280 + 2.31079i −2.50167 + 1.20474i −0.745806 − 0.935211i 4.02753 − 5.05037i −2.60944 + 0.436843i 1.05832 + 1.32709i −1.27631 + 5.59186i −1.63000 + 2.04396i
134.8 −0.477621 − 2.09259i −0.282352 − 0.354058i −2.34889 + 1.13116i 0.857192 + 1.07489i −0.606043 + 0.759954i −1.49942 + 2.17985i 0.812418 + 1.01874i 0.621928 − 2.72485i 1.83988 − 2.30714i
134.9 −0.475698 − 2.08417i 1.37920 + 1.72946i −2.31554 + 1.11511i −2.35614 − 2.95451i 2.94841 − 3.69718i 0.494705 + 2.59909i 0.759813 + 0.952775i −0.421280 + 1.84575i −5.03688 + 6.31605i
134.10 −0.435307 − 1.90720i −2.03711 − 2.55445i −1.64600 + 0.792670i 2.11340 + 2.65013i −3.98510 + 4.99715i 1.16867 − 2.37365i −0.211110 − 0.264723i −1.70786 + 7.48263i 4.13435 − 5.18431i
134.11 −0.429927 − 1.88363i −2.00383 − 2.51272i −1.56130 + 0.751882i −1.72332 − 2.16098i −3.87154 + 4.85476i 0.0600459 + 2.64507i −0.321742 − 0.403451i −1.63088 + 7.14533i −3.32959 + 4.17518i
134.12 −0.350704 − 1.53653i 0.400664 + 0.502417i −0.436007 + 0.209970i −0.520288 − 0.652421i 0.631466 − 0.791834i 2.25984 − 1.37591i −1.48977 − 1.86811i 0.575672 − 2.52218i −0.820000 + 1.02825i
134.13 −0.318166 − 1.39398i −1.31753 − 1.65213i −0.0400044 + 0.0192651i 0.0626586 + 0.0785714i −1.88384 + 2.36226i 2.64574 + 0.00599888i −1.74338 − 2.18613i −0.326091 + 1.42870i 0.0895909 − 0.112343i
134.14 −0.263441 − 1.15421i 0.200357 + 0.251240i 0.539140 − 0.259636i 0.720084 + 0.902957i 0.237201 − 0.297440i −2.13157 + 1.56729i −1.91799 − 2.40509i 0.644584 − 2.82411i 0.852501 − 1.06900i
134.15 −0.255883 − 1.12110i −1.45444 − 1.82381i 0.610554 − 0.294027i −1.13861 − 1.42777i −1.67250 + 2.09725i −2.29196 − 1.32171i −1.91980 − 2.40736i −0.543322 + 2.38045i −1.30932 + 1.64183i
134.16 −0.244792 − 1.07251i 1.93435 + 2.42560i 0.711593 − 0.342685i −0.681995 − 0.855194i 2.12795 − 2.66837i −0.00205300 − 2.64575i −1.91351 − 2.39947i −1.47425 + 6.45913i −0.750254 + 0.940788i
134.17 −0.210233 − 0.921093i 1.15175 + 1.44424i 0.997724 − 0.480479i 1.93087 + 2.42123i 1.08815 − 1.36449i −1.36392 − 2.26710i −1.83044 − 2.29530i −0.0917590 + 0.402022i 1.82425 − 2.28753i
134.18 −0.173372 − 0.759592i 0.660188 + 0.827850i 1.25502 − 0.604384i −0.00341729 − 0.00428515i 0.514370 − 0.645000i 0.479289 + 2.60198i −1.64822 − 2.06681i 0.418076 − 1.83171i −0.00266250 + 0.00333867i
134.19 −0.161553 − 0.707809i 0.573429 + 0.719058i 1.32704 − 0.639070i −2.43919 − 3.05864i 0.416317 − 0.522044i −2.50780 + 0.843173i −1.57205 − 1.97129i 0.479340 − 2.10013i −1.77088 + 2.22061i
134.20 −0.149857 − 0.656566i 1.79544 + 2.25141i 1.39332 − 0.670986i 1.83647 + 2.30286i 1.20914 − 1.51622i 1.90939 + 1.83146i −1.48912 − 1.86730i −1.17769 + 5.15978i 1.23677 − 1.55086i
See next 80 embeddings (of 264 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 134.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
49.e even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 931.2.u.b ✓ 264
49.e even 7 1 inner 931.2.u.b ✓ 264
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
931.2.u.b ✓ 264 1.a even 1 1 trivial
931.2.u.b ✓ 264 49.e even 7 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{264} + 3 T_{2}^{263} + 72 T_{2}^{262} + 214 T_{2}^{261} + 2780 T_{2}^{260} + \cdots + 24\!\cdots\!76 \) acting on \(S_{2}^{\mathrm{new}}(931, [\chi])\). Copy content Toggle raw display