↑

Properties

Label 87.5.l.a
Level $87$
Weight $5$
Character orbit 87.l
Analytic conductor $8.993$
Analytic rank $0$
Dimension $240$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [87,5,Mod(10,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.10"); S:= CuspForms(chi, 5); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([0, 23])) N = Newforms(chi, 5, names="a")
 
Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 87.l (of order \(28\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.99318678829\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(20\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240 q - 12 q^{2} + 12 q^{8} - 192 q^{10} + 192 q^{11} - 972 q^{14} - 396 q^{15} + 2808 q^{16} - 348 q^{17} + 324 q^{18} - 88 q^{19} - 5760 q^{20} + 2688 q^{22} + 3444 q^{23} + 1404 q^{24} + 7568 q^{25}+ \cdots - 5184 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
10.1 −6.02056 + 3.78297i −4.90456 − 1.71618i 14.9941 − 31.1357i 0.0311408 + 0.00710768i 36.0205 − 8.22143i 19.8697 − 9.56873i 14.7743 + 131.125i 21.1095 + 16.8342i −0.214373 + 0.0750124i
10.2 −5.85981 + 3.68196i 4.90456 + 1.71618i 13.8384 − 28.7357i −30.3259 − 6.92168i −35.0587 + 8.00192i 4.40684 − 2.12222i 12.3157 + 109.305i 21.1095 + 16.8342i 203.189 − 71.0989i
10.3 −4.83575 + 3.03850i −4.90456 − 1.71618i 7.20985 − 14.9714i −28.9857 − 6.61581i 28.9319 − 6.60351i −69.6215 + 33.5280i 0.394545 + 3.50169i 21.1095 + 16.8342i 160.270 − 56.0809i
10.4 −4.29822 + 2.70075i 4.90456 + 1.71618i 4.23850 − 8.80134i 5.67790 + 1.29594i −25.7159 + 5.86948i −32.2756 + 15.5431i −3.54162 − 31.4328i 21.1095 + 16.8342i −27.9049 + 9.76434i
10.5 −3.17385 + 1.99426i 4.90456 + 1.71618i −0.845901 + 1.75653i 30.4682 + 6.95416i −18.9889 + 4.33408i 50.7251 − 24.4279i −7.53320 − 66.8590i 21.1095 + 16.8342i −110.570 + 38.6901i
10.6 −2.44632 + 1.53712i −4.90456 − 1.71618i −3.32042 + 6.89492i 15.6259 + 3.56650i 14.6361 − 3.34059i 51.6425 − 24.8697i −7.65127 − 67.9069i 21.1095 + 16.8342i −43.7080 + 15.2941i
10.7 −2.18064 + 1.37019i 4.90456 + 1.71618i −4.06436 + 8.43973i −24.9666 − 5.69847i −13.0466 + 2.97780i −6.03736 + 2.90744i −7.31473 − 64.9200i 21.1095 + 16.8342i 62.2512 − 21.7826i
10.8 −1.81331 + 1.13938i −4.90456 − 1.71618i −4.95222 + 10.2834i −45.6220 − 10.4129i 10.8489 − 2.47619i 18.3539 − 8.83878i −6.57323 − 58.3390i 21.1095 + 16.8342i 94.5912 − 33.0989i
10.9 −1.06467 + 0.668979i −4.90456 − 1.71618i −6.25614 + 12.9910i 13.5284 + 3.08778i 6.36985 − 1.45388i −31.1219 + 14.9875i −4.28252 − 38.0084i 21.1095 + 16.8342i −16.4690 + 5.76277i
10.10 0.245098 − 0.154006i 4.90456 + 1.71618i −6.90578 + 14.3400i 34.6024 + 7.89777i 1.46640 − 0.334697i −84.2205 + 40.5585i 1.03440 + 9.18059i 21.1095 + 16.8342i 9.69729 − 3.39323i
10.11 0.833387 − 0.523652i 4.90456 + 1.71618i −6.52182 + 13.5427i −13.3679 − 3.05113i 4.98608 − 1.13804i 47.5345 − 22.8914i 3.41967 + 30.3504i 21.1095 + 16.8342i −12.7384 + 4.45734i
10.12 2.42819 − 1.52573i −4.90456 − 1.71618i −3.37389 + 7.00595i −5.90220 − 1.34714i −14.5277 + 3.31584i 75.6638 − 36.4378i 7.63415 + 67.7549i 21.1095 + 16.8342i −16.3871 + 5.73408i
10.13 2.90673 − 1.82642i −4.90456 − 1.71618i −1.82887 + 3.79768i 21.4117 + 4.88707i −17.3907 + 3.96932i −45.9559 + 22.1312i 7.76997 + 68.9604i 21.1095 + 16.8342i 71.1638 − 24.9013i
10.14 3.06494 − 1.92583i 4.90456 + 1.71618i −1.25709 + 2.61038i −38.2422 − 8.72854i 18.3373 − 4.18536i −72.0943 + 34.7188i 7.65879 + 67.9737i 21.1095 + 16.8342i −134.020 + 46.8956i
10.15 3.83545 − 2.40998i 4.90456 + 1.71618i 1.96059 − 4.07121i 18.7378 + 4.27678i 22.9472 − 5.23754i 21.2438 − 10.2305i 5.82299 + 51.6805i 21.1095 + 16.8342i 82.1748 − 28.7542i
10.16 3.91103 − 2.45746i −4.90456 − 1.71618i 2.31488 − 4.80690i −30.3144 − 6.91907i −23.3993 + 5.34074i 2.45060 − 1.18015i 5.51543 + 48.9508i 21.1095 + 16.8342i −135.564 + 47.4359i
10.17 5.52708 − 3.47289i −4.90456 − 1.71618i 11.5455 − 23.9744i 43.9888 + 10.0402i −33.0680 + 7.54756i 11.9244 − 5.74251i −7.75412 − 68.8197i 21.1095 + 16.8342i 277.998 − 97.2758i
10.18 5.84632 − 3.67349i 4.90456 + 1.71618i 13.7428 − 28.5373i −45.1701 − 10.3098i 34.9780 − 7.98351i 76.1888 − 36.6906i −12.1172 − 107.543i 21.1095 + 16.8342i −301.952 + 105.658i
10.19 6.20284 − 3.89750i −4.90456 − 1.71618i 16.3425 − 33.9357i −26.4112 − 6.02819i −37.1110 + 8.47035i −68.3409 + 32.9112i −17.7706 − 157.718i 21.1095 + 16.8342i −187.320 + 65.5460i
10.20 6.48256 − 4.07326i 4.90456 + 1.71618i 18.4900 − 38.3949i 21.1785 + 4.83385i 38.7846 − 8.85233i −40.6065 + 19.5550i −22.8146 − 202.486i 21.1095 + 16.8342i 156.980 − 54.9298i
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 10.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.f odd 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 87.5.l.a ✓ 240
29.f odd 28 1 inner 87.5.l.a ✓ 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
87.5.l.a ✓ 240 1.a even 1 1 trivial
87.5.l.a ✓ 240 29.f odd 28 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(87, [\chi])\).