↑

Properties

Label 1560.2.da
Level $1560$
Weight $2$
Character orbit 1560.da
Rep. character $\chi_{1560}(733,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $336$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.da (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 688 336 352
Cusp forms 656 336 320
Eisenstein series 32 0 32

Trace form

\( 336 q + O(q^{10}) \) \( 336 q + 8 q^{12} + 16 q^{17} - 20 q^{20} + 48 q^{22} - 16 q^{34} - 32 q^{40} + 16 q^{44} + 336 q^{49} + 56 q^{50} + 56 q^{52} + 48 q^{58} + 44 q^{60} + 72 q^{62} - 32 q^{65} - 32 q^{70} + 64 q^{71} - 32 q^{76} + 24 q^{78} + 36 q^{80} - 336 q^{81} - 8 q^{82} + 16 q^{86} + 8 q^{88} - 8 q^{90} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

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