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Properties

Label 1560.4.bq
Level $1560$
Weight $4$
Character orbit 1560.bq
Rep. character $\chi_{1560}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2000$
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.bq (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
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 2032 2032 0
Cusp forms 2000 2000 0
Eisenstein series 32 32 0

Trace form

\( 2000 q + O(q^{10}) \) \( 2000 q - 80 q^{10} - 112 q^{12} - 16 q^{16} - 160 q^{22} - 16 q^{25} + 496 q^{30} + 88 q^{36} - 920 q^{40} + 1000 q^{42} + 2548 q^{48} - 200 q^{52} + 1984 q^{55} - 1576 q^{66} - 4516 q^{78} - 16 q^{81} + 5064 q^{82} + 208 q^{87} - 2368 q^{88} + 2912 q^{90} + O(q^{100}) \)

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.