Properties

Level 24
Weight 12
Character $\chi_{24}(1, \cdot)$
Label 24.12.1.d
Dimension of Galois orbit 2
Twist info not available
CM No
Atkin-Lehner eigenvalues \( \omega_{ 2 } \) : -1
\( \omega_{ 3 } \) : -1

Related objects

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Show commands for: SageMath

magma: S := CuspForms(24,12);
magma: N := Newforms(S);
sage: N = Newforms(24,12,names="a")
sage: f = N[3]

q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
\(q \) \(\mathstrut+\) \(243q^{3} \) \(\mathstrut+\) \(\bigl(\frac{1}{2} \alpha \) \(\mathstrut+ 243\bigr)q^{5} \) \(\mathstrut+\) \(\bigl(- \frac{1}{2} \alpha \) \(\mathstrut+ 19427\bigr)q^{7} \) \(\mathstrut+\) \(59049q^{9} \) \(\mathstrut+O(q^{10}) \)
where
\(\alpha ^{2} \) \(\mathstrut -\mathstrut 2156 \alpha \) \(\mathstrut -\mathstrut 450200732\)\(\mathstrut=0\).


(To download coefficients, see below.)

Coefficient field

sage: K = f.hecke_eigenvalue_field() # note that sage often uses an isomorphic number field
The coefficient field is $\Q(\alpha)\cong\,$ \(\Q(\sqrt{3061}) \) where $ \alpha $ has minimal polynomial
\(x ^{2} \) \(\mathstrut -\mathstrut 2156 x \) \(\mathstrut -\mathstrut 450200732\)
over $\Q$.
sage: K.absolute_polynomial()

Embeddings

It is possible to embed the Fourier coefficients in the \(q\)-expansion above in the field of complex numbers. The different embeddings of the first few Fourier coefficients are shown in the table below. Note that these include embeddings that do not preserve the character.
\(n\) 2 3 4 5
\( v_{ 0 }(a(n)) \) 0.000000000000000 243.000000000000 0.000000000000000 -9840.65051670250
\( v_{ 1 }(a(n)) \) 0.000000000000000 243.000000000000 0.000000000000000 11404.6505167025

Detailed data

Further Properties

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 314 \).
Choose format to download:
Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 314)