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Properties

Label 1680.2.fc
Level $1680$
Weight $2$
Character orbit 1680.fc
Rep. character $\chi_{1680}(541,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $512$
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.fc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 512 1056
Cusp forms 1504 512 992
Eisenstein series 64 0 64

Trace form

\( 512 q - 8 q^{4} + O(q^{10}) \) \( 512 q - 8 q^{4} - 16 q^{11} - 32 q^{14} + 8 q^{16} + 8 q^{18} + 32 q^{20} - 64 q^{22} + 16 q^{28} + 64 q^{29} - 32 q^{37} + 80 q^{38} - 32 q^{43} + 24 q^{44} + 40 q^{46} + 16 q^{50} - 24 q^{52} + 32 q^{53} + 112 q^{56} + 48 q^{58} - 32 q^{59} + 64 q^{64} - 24 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{70} - 8 q^{72} + 8 q^{74} + 48 q^{78} + 256 q^{81} - 48 q^{84} - 104 q^{86} - 8 q^{88} + 16 q^{91} + 224 q^{92} - 120 q^{94} - 184 q^{98} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)