↑

Properties

Label 1680.2.ff
Level $1680$
Weight $2$
Character orbit 1680.ff
Rep. character $\chi_{1680}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.ff (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1680, [\chi])\).

Total New Old
Modular forms 1568 768 800
Cusp forms 1504 768 736
Eisenstein series 64 0 64

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 36 q^{10} + 32 q^{14} - 24 q^{35} + 60 q^{40} + 16 q^{44} - 24 q^{50} + 96 q^{59} + 24 q^{60} - 72 q^{66} + 60 q^{70} + 128 q^{71} - 40 q^{74} + 36 q^{80} + 384 q^{81} + 16 q^{86} - 32 q^{91} - 120 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)