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Properties

Label 1560.4.bh
Level $1560$
Weight $4$
Character orbit 1560.bh
Rep. character $\chi_{1560}(73,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $252$
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.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
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 252 1796
Cusp forms 1984 252 1732
Eisenstein series 64 0 64

Trace form

\( 252 q + 16 q^{5} + O(q^{10}) \) \( 252 q + 16 q^{5} + 56 q^{11} - 144 q^{13} + 156 q^{17} + 136 q^{19} - 156 q^{25} + 216 q^{31} + 24 q^{39} + 428 q^{41} - 252 q^{45} - 11724 q^{49} + 1716 q^{53} - 1872 q^{55} - 1096 q^{59} + 340 q^{65} + 2160 q^{67} + 3000 q^{73} - 624 q^{77} - 20412 q^{81} + 2964 q^{85} + 772 q^{89} + 5824 q^{95} - 336 q^{97} + 504 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)