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Properties

Label 2184.2.hb
Level $2184$
Weight $2$
Character orbit 2184.hb
Rep. character $\chi_{2184}(1003,\cdot)$
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.hb (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

\( 896 q - 448 q^{9} + O(q^{10}) \) \( 896 q - 448 q^{9} - 32 q^{14} + 32 q^{20} + 12 q^{24} + 20 q^{26} - 4 q^{28} + 40 q^{32} - 8 q^{34} + 120 q^{38} + 20 q^{40} - 12 q^{42} + 32 q^{44} - 48 q^{49} + 72 q^{50} + 72 q^{52} + 32 q^{57} + 48 q^{58} - 64 q^{59} + 28 q^{60} - 96 q^{70} - 32 q^{73} + 24 q^{78} - 36 q^{80} - 448 q^{81} + 16 q^{86} - 72 q^{88} + 160 q^{91} + 72 q^{92} + 12 q^{94} - 40 q^{96} - 32 q^{97} - 52 q^{98} + O(q^{100}) \)

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

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