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Properties

Label 1584.2.ck
Level $1584$
Weight $2$
Character orbit 1584.ck
Rep. character $\chi_{1584}(133,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $960$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

Total New Old
Modular forms 1168 960 208
Cusp forms 1136 960 176
Eisenstein series 32 0 32

Trace form

\( 960 q + 12 q^{6} + O(q^{10}) \) \( 960 q + 12 q^{6} - 24 q^{12} + 20 q^{18} - 28 q^{20} + 40 q^{24} - 24 q^{27} - 12 q^{30} + 40 q^{32} - 52 q^{36} - 56 q^{38} + 20 q^{42} - 48 q^{46} + 80 q^{47} - 32 q^{48} + 480 q^{49} + 52 q^{50} + 40 q^{51} - 40 q^{56} + 36 q^{58} - 24 q^{59} - 108 q^{60} - 24 q^{62} + 72 q^{64} + 20 q^{66} - 112 q^{72} - 56 q^{74} - 112 q^{75} - 24 q^{76} - 88 q^{78} + 72 q^{82} + 40 q^{83} + 152 q^{84} - 40 q^{86} - 20 q^{90} + 48 q^{93} - 212 q^{96} - 136 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)