Properties

Label 1440.1.cm
Level $1440$
Weight $1$
Character orbit 1440.cm
Rep. character $\chi_{1440}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $8$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1440.cm (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1440, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 8 8 0
Eisenstein series 32 8 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + O(q^{10}) \) \( 8 q + 8 q^{10} + 8 q^{61} - 8 q^{76} - 16 q^{79} + 8 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1440.1.cm.a $8$ $0.719$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}^{5}q^{5}+\cdots\)