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Properties

Label 1680.2.fp
Level $1680$
Weight $2$
Character orbit 1680.fp
Rep. character $\chi_{1680}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1504$
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.fp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1680 \)
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 1568 1568 0
Cusp forms 1504 1504 0
Eisenstein series 64 64 0

Trace form

\( 1504 q - 4 q^{3} - 16 q^{6} + O(q^{10}) \) \( 1504 q - 4 q^{3} - 16 q^{6} - 20 q^{10} + 10 q^{12} - 32 q^{13} - 16 q^{15} - 8 q^{16} - 10 q^{18} - 8 q^{21} - 32 q^{22} + 12 q^{24} - 16 q^{27} + 40 q^{28} + 30 q^{30} - 16 q^{31} - 4 q^{33} + 16 q^{36} - 8 q^{37} - 24 q^{39} - 44 q^{40} + 10 q^{42} - 22 q^{45} - 8 q^{46} + 4 q^{48} - 4 q^{51} + 20 q^{52} + 8 q^{54} + 24 q^{57} + 28 q^{58} + 12 q^{60} - 8 q^{61} + 20 q^{63} - 4 q^{66} - 24 q^{69} - 128 q^{70} + 34 q^{72} + 10 q^{75} - 32 q^{76} - 152 q^{78} - 8 q^{81} - 88 q^{82} - 60 q^{84} - 56 q^{85} + 12 q^{87} - 60 q^{88} - 96 q^{90} - 16 q^{91} + 20 q^{93} + 24 q^{94} - 76 q^{96} - 32 q^{97} + O(q^{100}) \)

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.