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Properties

Label 2160.4.t
Level $2160$
Weight $4$
Character orbit 2160.t
Rep. character $\chi_{2160}(541,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $768$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).

Total New Old
Modular forms 2616 768 1848
Cusp forms 2568 768 1800
Eisenstein series 48 0 48

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 60 q^{10} + 828 q^{16} + 24 q^{19} + 504 q^{22} + 72 q^{28} - 348 q^{34} - 1344 q^{46} - 37632 q^{49} + 792 q^{52} + 7104 q^{58} - 912 q^{61} - 1512 q^{64} + 6528 q^{67} - 4416 q^{76} + 2832 q^{79} + 2280 q^{82} - 240 q^{85} + 11304 q^{88} - 3600 q^{91} + 6468 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)