Properties

Label 1440.1.y
Level $1440$
Weight $1$
Character orbit 1440.y
Rep. character $\chi_{1440}(433,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 80 8 72
Cusp forms 16 4 12
Eisenstein series 64 4 60

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 4 q^{7} + O(q^{10}) \) \( 4 q + 4 q^{7} + 4 q^{55} + 4 q^{73} - 4 q^{97} + O(q^{100}) \)

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.y.a $4$ $0.719$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)