Properties

Label 1280.1.p
Level $1280$
Weight $1$
Character orbit 1280.p
Rep. character $\chi_{1280}(257,\cdot)$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 66 12 54
Cusp forms 18 4 14
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.p.a 1280.p 5.c $2$ $0.639$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None 640.1.m.a \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-iq^{9}+(1+i)q^{13}+(1-i)q^{17}+\cdots\)
1280.1.p.b 1280.p 5.c $2$ $0.639$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None 640.1.m.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

\( S_{1}^{\mathrm{old}}(1280, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)