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Properties

Label 2160.2.bg
Level $2160$
Weight $2$
Character orbit 2160.bg
Rep. character $\chi_{2160}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.bg (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

Total New Old
Modular forms 888 384 504
Cusp forms 840 384 456
Eisenstein series 48 0 48

Trace form

\( 384 q + 4 q^{4} + O(q^{10}) \) \( 384 q + 4 q^{4} - 4 q^{16} + 8 q^{19} - 8 q^{22} + 16 q^{28} + 32 q^{34} - 20 q^{40} + 32 q^{46} - 28 q^{52} - 8 q^{58} - 16 q^{61} - 32 q^{64} + 80 q^{70} + 32 q^{76} - 68 q^{82} - 40 q^{88} + 20 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

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