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Properties

Label 2160.2.ep
Level $2160$
Weight $2$
Character orbit 2160.ep
Rep. character $\chi_{2160}(11,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $3456$
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.ep (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 5232 3456 1776
Cusp forms 5136 3456 1680
Eisenstein series 96 0 96

Trace form

\( 3456 q + O(q^{10}) \) \( 3456 q - 36 q^{12} + 60 q^{24} - 120 q^{42} + 168 q^{54} + 108 q^{58} - 72 q^{59} + 396 q^{62} - 96 q^{66} + 156 q^{68} + 168 q^{72} + 168 q^{74} + 156 q^{78} + 120 q^{83} + 132 q^{84} - 108 q^{96} + O(q^{100}) \)

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

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