Properties

Label 2880.1.ec
Level $2880$
Weight $1$
Character orbit 2880.ec
Rep. character $\chi_{2880}(19,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $16$
Newform subspaces $1$
Sturm bound $576$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2880.ec (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
Sturm bound: \(576\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2880, [\chi])\).

Total New Old
Modular forms 80 32 48
Cusp forms 16 16 0
Eisenstein series 64 16 48

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

\( 16 q + O(q^{10}) \) \( 16 q - 16 q^{76} + 16 q^{79} - 16 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2880.1.ec.a 2880.ec 320.ah $16$ $1.437$ \(\Q(\zeta_{32})\) $D_{16}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{7}q^{2}+\zeta_{32}^{14}q^{4}-\zeta_{32}q^{5}+\cdots\)