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Properties

Label 2184.2.hw
Level $2184$
Weight $2$
Character orbit 2184.hw
Rep. character $\chi_{2184}(397,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $896$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2184.hw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 728 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2184, [\chi])\).

Total New Old
Modular forms 1824 896 928
Cusp forms 1760 896 864
Eisenstein series 64 0 64

Trace form

\( 896 q + 896 q^{9} + O(q^{10}) \) \( 896 q + 896 q^{9} + 32 q^{14} + 60 q^{26} + 8 q^{28} - 20 q^{32} - 60 q^{40} - 24 q^{42} - 16 q^{44} - 20 q^{46} + 72 q^{50} + 108 q^{52} - 108 q^{56} - 32 q^{57} + 24 q^{58} - 4 q^{60} + 64 q^{71} + 48 q^{73} - 24 q^{78} + 896 q^{81} - 16 q^{86} - 72 q^{92} - 60 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2184, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2184, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)