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Properties

Label 1680.2.fv
Level $1680$
Weight $2$
Character orbit 1680.fv
Rep. character $\chi_{1680}(493,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
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.fv (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

\( 768 q + 24 q^{8} - 384 q^{9} + O(q^{10}) \) \( 768 q + 24 q^{8} - 384 q^{9} - 20 q^{28} - 16 q^{30} + 24 q^{35} + 36 q^{38} + 60 q^{40} - 20 q^{42} - 48 q^{44} + 108 q^{52} - 8 q^{58} - 96 q^{59} + 72 q^{66} + 48 q^{67} - 132 q^{68} + 24 q^{70} - 12 q^{72} - 48 q^{78} - 384 q^{81} + 60 q^{82} + 24 q^{84} - 16 q^{86} - 68 q^{88} - 32 q^{91} - 72 q^{92} + 72 q^{94} + 48 q^{95} - 144 q^{98} + O(q^{100}) \)

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

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