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Properties

Label 1680.2.dv
Level $1680$
Weight $2$
Character orbit 1680.dv
Rep. character $\chi_{1680}(1361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
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.dv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 816 128 688
Cusp forms 720 128 592
Eisenstein series 96 0 96

Trace form

\( 128 q + 4 q^{7} + O(q^{10}) \) \( 128 q + 4 q^{7} - 12 q^{19} - 4 q^{21} - 64 q^{25} - 84 q^{31} - 12 q^{39} + 56 q^{43} + 12 q^{45} - 8 q^{49} + 32 q^{51} + 40 q^{63} - 28 q^{67} + 24 q^{73} + 36 q^{79} + 4 q^{81} + 108 q^{87} + 12 q^{91} - 16 q^{93} - 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)