Properties

Label 1280.1.e
Level $1280$
Weight $1$
Character orbit 1280.e
Rep. character $\chi_{1280}(639,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1280.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 38 6 32
Cusp forms 14 2 12
Eisenstein series 24 4 20

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{9} - 2 q^{25} + 4 q^{41} - 2 q^{49} + 2 q^{81} - 4 q^{89} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.1.e.a 1280.e 40.e $2$ $0.639$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+q^{9}-q^{25}-iq^{29}+q^{41}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1280, [\chi]) \cong \)