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Properties

Label 7.24.c.a
Level $7$
Weight $24$
Character orbit 7.c
Analytic conductor $23.464$
Analytic rank $0$
Dimension $28$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7,24,Mod(2,7)] 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("7.2"); S:= CuspForms(chi, 24); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 24, names="a")
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\), degree \(2\), 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: \(23.4642826142\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 966 q^{2} - 177148 q^{3} - 55357148 q^{4} - 74771022 q^{5} + 3009216508 q^{6} + 654254272 q^{7} + 50444801232 q^{8} - 336909608980 q^{9} - 334296297894 q^{10} + 1355476566108 q^{11} - 4984668058916 q^{12}+ \cdots - 46\!\cdots\!68 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −2850.44 + 4937.11i −209916. − 363586.i −1.20557e7 − 2.08812e7i −3.17471e7 + 5.49875e7i 2.39342e9 3.14280e8 + 5.22207e9i 8.96344e10 −4.10583e10 + 7.11150e10i −1.80986e11 − 3.13478e11i
2.2 −2240.10 + 3879.97i 84864.7 + 146990.i −5.84181e6 − 1.01183e7i 4.26595e7 − 7.38885e7i −7.60422e8 −4.40176e9 − 2.82723e9i 1.47623e10 3.26676e10 − 5.65819e10i 1.91123e11 + 3.31035e11i
2.3 −2080.04 + 3602.74i 152288. + 263771.i −4.45884e6 − 7.72294e6i −5.11115e7 + 8.85278e7i −1.26706e9 5.23125e9 + 5.27080e7i 2.20102e9 6.88244e8 − 1.19207e9i −2.12628e11 − 3.68283e11i
2.4 −1286.90 + 2228.97i −134187. − 232418.i 882091. + 1.52783e6i 8.56874e7 − 1.48415e8i 6.90739e8 3.36174e9 + 4.00842e9i −2.61312e10 1.10594e10 − 1.91554e10i 2.20542e11 + 3.81990e11i
2.5 −1256.79 + 2176.82i −192681. − 333734.i 1.03526e6 + 1.79313e6i −3.60011e7 + 6.23558e7i 9.68640e8 −1.43544e9 − 5.03073e9i −2.62899e10 −2.71807e10 + 4.70783e10i −9.04917e10 − 1.56736e11i
2.6 −643.722 + 1114.96i 268410. + 464900.i 3.36555e6 + 5.82930e6i 2.50795e7 − 4.34389e7i −6.91126e8 −3.38128e9 + 3.99196e9i −1.94658e10 −9.70166e10 + 1.68038e11i 3.22884e10 + 5.59251e10i
2.7 −409.258 + 708.856i −13709.4 − 23745.5i 3.85932e6 + 6.68454e6i −9.14709e7 + 1.58432e8i 2.24428e7 −2.59623e9 + 4.54184e9i −1.31840e10 4.66957e10 − 8.08793e10i −7.48705e10 − 1.29679e11i
2.8 354.185 − 613.466i 99138.9 + 171714.i 3.94341e6 + 6.83019e6i 1.81832e7 − 3.14943e7i 1.40454e8 3.51978e9 − 3.87038e9i 1.15290e10 2.74145e10 − 4.74834e10i −1.28804e10 − 2.23096e10i
2.9 1014.57 − 1757.29i −116452. − 201701.i 2.13559e6 + 3.69896e6i 4.66998e7 − 8.08863e7i −4.72597e8 −5.17266e9 + 7.82494e8i 2.56885e10 1.99493e10 − 3.45533e10i −9.47605e10 − 1.64130e11i
2.10 1150.44 − 1992.62i −293195. − 507829.i 1.54728e6 + 2.67997e6i −2.34581e7 + 4.06307e7i −1.34921e9 5.21199e9 + 4.51604e8i 2.64214e10 −1.24855e11 + 2.16256e11i 5.39743e10 + 9.34863e10i
2.11 1838.54 − 3184.45i 232883. + 403365.i −2.56619e6 − 4.44477e6i −6.91642e7 + 1.19796e8i 1.71266e9 −3.84342e9 − 3.54920e9i 1.19734e10 −6.13975e10 + 1.06344e11i 2.54323e11 + 4.40500e11i
2.12 1989.65 − 3446.18i −12284.6 − 21277.5i −3.72314e6 − 6.44867e6i −5.96803e7 + 1.03369e8i −9.77681e7 3.21228e9 + 4.12917e9i 3.74979e9 4.67698e10 − 8.10076e10i 2.37486e11 + 4.11339e11i
2.13 2256.55 − 3908.45i 176588. + 305860.i −5.98971e6 − 1.03745e7i 9.71323e7 − 1.68238e8i 1.59392e9 2.22602e9 + 4.73430e9i −1.62057e10 −1.52953e10 + 2.64922e10i −4.38367e11 − 7.59274e11i
2.14 2646.31 − 4583.55i −130321. − 225723.i −9.81164e6 − 1.69943e7i 9.80623e6 − 1.69849e7i −1.37948e9 −1.91940e9 − 4.86669e9i −5.94609e10 1.31044e10 − 2.26975e10i −5.19007e10 − 8.98947e10i
4.1 −2850.44 − 4937.11i −209916. + 363586.i −1.20557e7 + 2.08812e7i −3.17471e7 − 5.49875e7i 2.39342e9 3.14280e8 − 5.22207e9i 8.96344e10 −4.10583e10 − 7.11150e10i −1.80986e11 + 3.13478e11i
4.2 −2240.10 − 3879.97i 84864.7 − 146990.i −5.84181e6 + 1.01183e7i 4.26595e7 + 7.38885e7i −7.60422e8 −4.40176e9 + 2.82723e9i 1.47623e10 3.26676e10 + 5.65819e10i 1.91123e11 − 3.31035e11i
4.3 −2080.04 − 3602.74i 152288. − 263771.i −4.45884e6 + 7.72294e6i −5.11115e7 − 8.85278e7i −1.26706e9 5.23125e9 − 5.27080e7i 2.20102e9 6.88244e8 + 1.19207e9i −2.12628e11 + 3.68283e11i
4.4 −1286.90 − 2228.97i −134187. + 232418.i 882091. − 1.52783e6i 8.56874e7 + 1.48415e8i 6.90739e8 3.36174e9 − 4.00842e9i −2.61312e10 1.10594e10 + 1.91554e10i 2.20542e11 − 3.81990e11i
4.5 −1256.79 − 2176.82i −192681. + 333734.i 1.03526e6 − 1.79313e6i −3.60011e7 − 6.23558e7i 9.68640e8 −1.43544e9 + 5.03073e9i −2.62899e10 −2.71807e10 − 4.70783e10i −9.04917e10 + 1.56736e11i
4.6 −643.722 − 1114.96i 268410. − 464900.i 3.36555e6 − 5.82930e6i 2.50795e7 + 4.34389e7i −6.91126e8 −3.38128e9 − 3.99196e9i −1.94658e10 −9.70166e10 − 1.68038e11i 3.22884e10 − 5.59251e10i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7.24.c.a ✓ 28
7.c even 3 1 inner 7.24.c.a ✓ 28
7.c even 3 1 49.24.a.g 14
7.d odd 6 1 49.24.a.f 14
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.24.c.a ✓ 28 1.a even 1 1 trivial
7.24.c.a ✓ 28 7.c even 3 1 inner
49.24.a.f 14 7.d odd 6 1
49.24.a.g 14 7.c even 3 1

Hecke kernels

This newform subspace is the entire newspace \(S_{24}^{\mathrm{new}}(7, [\chi])\).