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Properties

Label 1680.2.ca
Level $1680$
Weight $2$
Character orbit 1680.ca
Rep. character $\chi_{1680}(491,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.ca (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 784 384 400
Cusp forms 752 384 368
Eisenstein series 32 0 32

Trace form

\( 384 q - 24 q^{6} + O(q^{10}) \) \( 384 q - 24 q^{6} + 8 q^{10} - 24 q^{12} + 40 q^{16} - 16 q^{19} + 32 q^{24} + 48 q^{27} + 8 q^{34} - 24 q^{36} + 96 q^{39} - 120 q^{46} + 384 q^{49} - 64 q^{52} + 176 q^{58} + 32 q^{61} + 144 q^{64} + 32 q^{66} + 64 q^{67} + 56 q^{72} - 8 q^{76} + 80 q^{78} + 64 q^{82} + 32 q^{85} - 48 q^{88} + 96 q^{93} - 8 q^{94} + 32 q^{96} - 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)