↑

Properties

Label 1560.4.cm
Level $1560$
Weight $4$
Character orbit 1560.cm
Rep. character $\chi_{1560}(941,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1344$
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.cm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
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 1344 688
Cusp forms 2000 1344 656
Eisenstein series 32 0 32

Trace form

\( 1344 q - 60 q^{6} + O(q^{10}) \) \( 1344 q - 60 q^{6} + 372 q^{18} + 368 q^{24} + 72 q^{28} + 360 q^{34} + 680 q^{42} + 1440 q^{46} - 40 q^{48} - 3672 q^{52} - 1072 q^{54} - 2664 q^{58} - 4560 q^{66} - 1532 q^{72} - 864 q^{73} + 4440 q^{76} + 2532 q^{78} + 4948 q^{84} + 16224 q^{87} + 9360 q^{94} + 2900 q^{96} - 3168 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)