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Properties

Label 2160.4.bc
Level $2160$
Weight $4$
Character orbit 2160.bc
Rep. character $\chi_{2160}(917,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1152$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
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 1152 1464
Cusp forms 2568 1152 1416
Eisenstein series 48 0 48

Trace form

\( 1152 q + 12 q^{4} + O(q^{10}) \) \( 1152 q + 12 q^{4} - 132 q^{16} + 24 q^{19} - 216 q^{22} + 432 q^{28} + 1056 q^{34} + 780 q^{40} + 864 q^{43} + 96 q^{46} - 996 q^{52} - 360 q^{58} + 912 q^{61} + 1824 q^{64} - 5040 q^{70} + 2976 q^{76} - 3084 q^{82} + 4776 q^{88} + 420 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)