Properties

Label 3584.1.bf
Level $3584$
Weight $1$
Character orbit 3584.bf
Rep. character $\chi_{3584}(97,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $16$
Newform subspaces $2$
Sturm bound $512$
Trace bound $63$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3584.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(512\)
Trace bound: \(63\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3584, [\chi])\).

Total New Old
Modular forms 192 48 144
Cusp forms 64 16 48
Eisenstein series 128 32 96

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + O(q^{10}) \) \( 16 q + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3584.1.bf.a 3584.bf 448.af $8$ $1.789$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(\zeta_{16}^{3}+\zeta_{16}^{6}+\cdots)q^{11}+\cdots\)
3584.1.bf.b 3584.bf 448.af $8$ $1.789$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(-\zeta_{16}^{3}-\zeta_{16}^{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)