Properties

Label 560.1.bt
Level $560$
Weight $1$
Character orbit 560.bt
Rep. character $\chi_{560}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 560.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(560, [\chi])\).

Total New Old
Modular forms 40 4 36
Cusp forms 16 4 12
Eisenstein series 24 0 24

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 0

Trace form

\( 4q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 4q + 2q^{5} - 4q^{9} - 6q^{21} - 2q^{25} - 4q^{29} + 4q^{41} + 4q^{45} + 2q^{49} - 2q^{61} + 12q^{69} - 2q^{81} + 2q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
560.1.bt.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)