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Properties

Label 2160.4.dv
Level $2160$
Weight $4$
Character orbit 2160.dv
Rep. character $\chi_{2160}(61,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $10368$
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.dv (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 15600 10368 5232
Cusp forms 15504 10368 5136
Eisenstein series 96 0 96

Trace form

\( 10368 q + O(q^{10}) \) \( 10368 q + 468 q^{12} - 1500 q^{24} + 9480 q^{42} + 8904 q^{54} + 3564 q^{58} + 6120 q^{59} - 2508 q^{62} + 9888 q^{66} - 9204 q^{68} - 11928 q^{72} - 10920 q^{74} - 4524 q^{78} - 7320 q^{83} + 11220 q^{84} - 5076 q^{96} + O(q^{100}) \)

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

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