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Properties

Label 1680.2.cb
Level $1680$
Weight $2$
Character orbit 1680.cb
Rep. character $\chi_{1680}(589,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.cb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 784 288 496
Cusp forms 752 288 464
Eisenstein series 32 0 32

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 8 q^{16} - 16 q^{19} + 8 q^{24} + 80 q^{26} + 16 q^{30} - 8 q^{34} + 8 q^{36} - 40 q^{40} + 112 q^{44} + 8 q^{46} + 288 q^{49} + 40 q^{50} - 16 q^{51} + 8 q^{54} - 48 q^{56} + 24 q^{60} - 32 q^{61} - 48 q^{64} - 32 q^{65} + 32 q^{69} + 24 q^{70} + 48 q^{74} + 32 q^{75} - 72 q^{76} + 192 q^{79} - 80 q^{80} - 288 q^{81} - 64 q^{86} - 16 q^{90} - 88 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)