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Properties

Label 1680.2.gc
Level $1680$
Weight $2$
Character orbit 1680.gc
Rep. character $\chi_{1680}(737,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
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.gc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
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 1632 400 1232
Cusp forms 1440 368 1072
Eisenstein series 192 32 160

Trace form

\( 368 q + 2 q^{3} + 8 q^{7} + O(q^{10}) \) \( 368 q + 2 q^{3} + 8 q^{7} - 16 q^{13} + 8 q^{15} - 4 q^{25} + 8 q^{27} + 8 q^{31} - 14 q^{33} - 4 q^{37} + 16 q^{43} + 18 q^{45} + 28 q^{51} + 56 q^{55} + 12 q^{57} - 8 q^{61} + 54 q^{63} + 4 q^{67} - 20 q^{73} + 2 q^{75} + 4 q^{81} - 16 q^{85} + 8 q^{87} + 112 q^{91} + 10 q^{93} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)