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Properties

Label 2160.4.dm
Level $2160$
Weight $4$
Character orbit 2160.dm
Rep. character $\chi_{2160}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1932$
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.dm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 7848 1956 5892
Cusp forms 7704 1932 5772
Eisenstein series 144 24 120

Trace form

\( 1932 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 1932 q - 6 q^{5} - 12 q^{9} + 12 q^{11} + 6 q^{15} + 6 q^{19} - 12 q^{21} - 6 q^{25} + 72 q^{29} + 12 q^{31} + 3 q^{35} + 840 q^{39} - 12 q^{41} - 6 q^{45} - 12 q^{49} + 174 q^{51} + 12 q^{55} + 12 q^{59} - 12 q^{61} + 690 q^{65} - 12 q^{69} - 5958 q^{71} + 2484 q^{75} + 12 q^{79} + 900 q^{81} - 381 q^{85} - 6 q^{89} + 6 q^{91} + 4923 q^{95} + 12 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)