Properties

Label 1568.1.o
Level $1568$
Weight $1$
Character orbit 1568.o
Rep. character $\chi_{1568}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1568.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).

Total New Old
Modular forms 88 14 74
Cusp forms 24 6 18
Eisenstein series 64 8 56

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

\( 6 q - q^{9} + O(q^{10}) \) \( 6 q - q^{9} - 2 q^{11} - 3 q^{25} + 4 q^{43} - 4 q^{51} - 8 q^{57} - 2 q^{67} + q^{81} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1568.1.o.a 1568.o 56.k $2$ $0.783$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{25}+q^{43}+\cdots\)
1568.1.o.b 1568.o 56.k $4$ $0.783$ \(\Q(\sqrt{2}, \sqrt{-3})\) $D_{4}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{3}+(-1-\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)