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Properties

Label 1600.1.bh
Level $1600$
Weight $1$
Character orbit 1600.bh
Rep. character $\chi_{1600}(191,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $12$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 96 20 76
Cusp forms 48 12 36
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 8

Trace form

\( 12 q + 3 q^{5} - q^{9} + O(q^{10}) \) \( 12 q + 3 q^{5} - q^{9} - 4 q^{13} - 2 q^{17} - 4 q^{21} - 3 q^{25} + 8 q^{29} - 5 q^{37} - 2 q^{41} + q^{45} - 5 q^{53} - 4 q^{57} + 4 q^{61} - q^{65} - 2 q^{69} - 4 q^{73} + q^{81} - 3 q^{85} + 3 q^{89} + 8 q^{93} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bh.a 1600.bh 100.j $4$ $0.799$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
1600.1.bh.b 1600.bh 100.j $8$ $0.799$ \(\Q(\zeta_{20})\) $A_{5}$ None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{20}^{9}q^{3}-\zeta_{20}^{8}q^{5}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)