Properties

Label 1680.2.eg
Level $1680$
Weight $2$
Character orbit 1680.eg
Rep. character $\chi_{1680}(689,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
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.eg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 816 200 616
Cusp forms 720 184 536
Eisenstein series 96 16 80

Trace form

\( 184 q - 2 q^{9} + O(q^{10}) \) \( 184 q - 2 q^{9} + 10 q^{15} + 12 q^{19} + 6 q^{21} + 2 q^{25} + 12 q^{31} - 4 q^{39} - 3 q^{45} - 16 q^{49} + 2 q^{51} - 12 q^{61} + 57 q^{75} + 28 q^{79} - 22 q^{81} - 44 q^{85} + 16 q^{91} + 68 q^{99} + O(q^{100}) \)

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

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