Properties

Label 1680.2.cy
Level $1680$
Weight $2$
Character orbit 1680.cy
Rep. character $\chi_{1680}(1007,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.cy (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 816 192 624
Cusp forms 720 192 528
Eisenstein series 96 0 96

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 24 q^{21} + 48 q^{57} + 48 q^{81} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)