Properties

Label 1568.1.bl
Level $1568$
Weight $1$
Character orbit 1568.bl
Rep. character $\chi_{1568}(117,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $8$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1568.bl (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 72 40 32
Cusp forms 8 8 0
Eisenstein series 64 32 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + O(q^{10}) \) \( 8 q + 4 q^{16} + 4 q^{18} + 8 q^{22} + 4 q^{23} - 8 q^{43} - 4 q^{44} + 4 q^{53} - 4 q^{67} - 4 q^{74} - 8 q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1568.1.bl.a $8$ $0.783$ \(\Q(\zeta_{24})\) $D_{8}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{3}q^{8}+\cdots\)