Properties

Label 1560.2.fp
Level $1560$
Weight $2$
Character orbit 1560.fp
Rep. character $\chi_{1560}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $672$
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.fp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 672 704
Cusp forms 1312 672 640
Eisenstein series 64 0 64

Trace form

\( 672 q + O(q^{10}) \) \( 672 q + 8 q^{10} + 16 q^{12} + 16 q^{16} - 8 q^{17} - 12 q^{22} + 16 q^{25} - 16 q^{26} + 8 q^{30} + 60 q^{32} - 64 q^{40} - 20 q^{42} - 32 q^{43} + 48 q^{50} + 16 q^{52} - 32 q^{56} + 72 q^{58} - 4 q^{62} - 16 q^{65} + 24 q^{78} + 336 q^{81} + 32 q^{82} - 32 q^{88} + 128 q^{91} - 104 q^{92} + O(q^{100}) \)

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

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