Properties

Label 1568.1.g
Level $1568$
Weight $1$
Character orbit 1568.g
Rep. character $\chi_{1568}(687,\cdot)$
Character field $\Q$
Dimension $3$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
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 44 8 36
Cusp forms 12 3 9
Eisenstein series 32 5 27

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

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

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.g.a 1568.g 8.d $1$ $0.783$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}+2q^{11}+q^{25}+2q^{43}-2q^{67}+\cdots\)
1568.1.g.b 1568.g 8.d $2$ $0.783$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+q^{9}-\beta q^{17}+\beta q^{19}+q^{25}+\cdots\)

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

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