Properties

Label 1680.2.ce
Level $1680$
Weight $2$
Character orbit 1680.ce
Rep. character $\chi_{1680}(811,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $256$
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.ce (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 784 256 528
Cusp forms 752 256 496
Eisenstein series 32 0 32

Trace form

\( 256 q + 8 q^{4} + O(q^{10}) \) \( 256 q + 8 q^{4} - 16 q^{11} + 16 q^{14} - 8 q^{16} + 8 q^{18} + 56 q^{22} + 32 q^{23} - 64 q^{28} - 32 q^{29} - 32 q^{37} + 16 q^{43} + 40 q^{44} + 80 q^{46} + 8 q^{50} - 32 q^{53} + 56 q^{56} + 120 q^{58} + 56 q^{64} - 16 q^{67} + 16 q^{70} + 128 q^{71} - 8 q^{72} - 8 q^{74} + 48 q^{78} - 256 q^{81} + 48 q^{84} - 152 q^{86} - 8 q^{88} + 16 q^{91} - 128 q^{92} + 16 q^{98} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)