Properties

Label 1280.1.m
Level $1280$
Weight $1$
Character orbit 1280.m
Rep. character $\chi_{1280}(897,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1280.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1280, [\chi])\).

Total New Old
Modular forms 60 12 48
Cusp forms 12 4 8
Eisenstein series 48 8 40

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

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{17} + 4 q^{25} + 4 q^{65} - 4 q^{73} - 4 q^{81} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.1.m.a 1280.m 40.i $2$ $0.639$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None 160.1.p.a \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
1280.1.m.b 1280.m 40.i $2$ $0.639$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None 160.1.p.a \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+iq^{9}+(1-i)q^{13}+(-1+i+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1280, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)