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Properties

Label 2160.2.bl
Level $2160$
Weight $2$
Character orbit 2160.bl
Rep. character $\chi_{2160}(971,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $256$
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.bl (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 888 256 632
Cusp forms 840 256 584
Eisenstein series 48 0 48

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 4 q^{10} + 60 q^{16} + 8 q^{19} - 24 q^{22} - 24 q^{28} - 4 q^{34} + 256 q^{49} + 8 q^{52} + 64 q^{58} - 16 q^{61} - 24 q^{64} + 128 q^{67} + 64 q^{76} + 40 q^{82} - 16 q^{85} + 104 q^{88} + 48 q^{91} + 28 q^{94} + O(q^{100}) \)

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

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