Properties

Label 1600.1.p
Level $1600$
Weight $1$
Character orbit 1600.p
Rep. character $\chi_{1600}(193,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1600.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 102 10 92
Cusp forms 30 6 24
Eisenstein series 72 4 68

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q - 2 q^{13} + 2 q^{17} + 8 q^{21} + 2 q^{37} + 2 q^{53} - 2 q^{73} + 2 q^{81} - 2 q^{97} + O(q^{100}) \)

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.p.a 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q+(-1+i)q^{3}+(-1-i)q^{7}-iq^{9}+\cdots\)
1600.1.p.b 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{9}+(-1+i)q^{13}+(1+i)q^{17}+\cdots\)
1600.1.p.c 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(2\) \(q+(1-i)q^{3}+(1+i)q^{7}-iq^{9}+q^{21}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)