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Properties

Label 2160.2.cg
Level $2160$
Weight $2$
Character orbit 2160.cg
Rep. character $\chi_{2160}(251,\cdot)$
Character field $\Q(\zeta_{12})$
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.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1776 384 1392
Cusp forms 1680 384 1296
Eisenstein series 96 0 96

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 24 q^{46} - 192 q^{49} - 36 q^{58} - 72 q^{59} + 72 q^{64} + 156 q^{68} + 168 q^{74} + 12 q^{76} + 72 q^{82} + 120 q^{83} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)