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Properties

Label 1560.4.el
Level $1560$
Weight $4$
Character orbit 1560.el
Rep. character $\chi_{1560}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2016$
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.el (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4064 2016 2048
Cusp forms 4000 2016 1984
Eisenstein series 64 0 64

Trace form

\( 2016 q + O(q^{10}) \) \( 2016 q - 48 q^{12} - 104 q^{17} - 380 q^{20} - 476 q^{22} - 1020 q^{32} - 1504 q^{34} - 264 q^{40} + 1980 q^{42} - 1232 q^{44} - 49392 q^{49} - 4948 q^{50} + 1608 q^{52} - 1368 q^{58} + 2064 q^{60} - 468 q^{62} - 344 q^{65} + 408 q^{70} + 448 q^{71} - 7008 q^{74} - 2144 q^{76} - 72 q^{78} - 1476 q^{80} + 81648 q^{81} + 1656 q^{82} - 5312 q^{86} + 3072 q^{88} + 1296 q^{90} + O(q^{100}) \)

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.

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)