Properties

Label 1600.1.bf
Level $1600$
Weight $1$
Character orbit 1600.bf
Rep. character $\chi_{1600}(319,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1600.bf (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).

Total New Old
Modular forms 64 12 52
Cusp forms 16 4 12
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

\( 4 q - q^{5} + q^{9} + O(q^{10}) \) \( 4 q - q^{5} + q^{9} - q^{25} + 2 q^{29} + 5 q^{37} + 2 q^{41} + q^{45} - 4 q^{49} + 5 q^{53} - 2 q^{61} - 5 q^{65} - q^{81} - 5 q^{85} + 3 q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.1.bf.a 1600.bf 100.h $4$ $0.799$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)