↑

Properties

Label 1560.4.dx
Level $1560$
Weight $4$
Character orbit 1560.dx
Rep. character $\chi_{1560}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1560.dx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2048 256 1792
Cusp forms 1984 256 1728
Eisenstein series 64 0 64

Trace form

\( 256 q - 16 q^{5} + 1152 q^{9} + O(q^{10}) \) \( 256 q - 16 q^{5} + 1152 q^{9} - 28 q^{11} - 68 q^{19} + 144 q^{25} - 296 q^{29} + 216 q^{31} - 12 q^{39} - 304 q^{41} - 72 q^{45} + 6900 q^{49} - 2448 q^{51} + 468 q^{55} + 1096 q^{59} - 400 q^{61} - 188 q^{65} + 1104 q^{69} - 312 q^{75} + 3960 q^{79} - 10368 q^{81} + 2544 q^{85} + 4756 q^{89} + 3652 q^{91} - 440 q^{95} - 504 q^{99} + O(q^{100}) \)

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

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