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Properties

Label 1560.4.by
Level $1560$
Weight $4$
Character orbit 1560.by
Rep. character $\chi_{1560}(1409,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $504$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1560.by (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1560, [\chi])\).

Total New Old
Modular forms 2048 504 1544
Cusp forms 1984 504 1480
Eisenstein series 64 0 64

Trace form

\( 504 q + O(q^{10}) \) \( 504 q + 88 q^{15} - 216 q^{31} + 424 q^{39} + 228 q^{45} + 1872 q^{55} + 3744 q^{61} - 1872 q^{79} + 272 q^{81} + 120 q^{85} + 288 q^{91} + 3728 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)