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Properties

Label 1584.2.cg
Level $1584$
Weight $2$
Character orbit 1584.cg
Rep. character $\chi_{1584}(461,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1136$
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.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1584 \)
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 1168 0
Cusp forms 1136 1136 0
Eisenstein series 32 32 0

Trace form

\( 1136 q - 8 q^{3} - 4 q^{4} - 12 q^{5} + O(q^{10}) \) \( 1136 q - 8 q^{3} - 4 q^{4} - 12 q^{5} - 6 q^{11} - 8 q^{12} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 12 q^{20} - 2 q^{22} - 8 q^{27} - 8 q^{31} - 8 q^{33} - 12 q^{34} - 24 q^{36} - 16 q^{37} - 12 q^{38} + 36 q^{42} + 12 q^{45} - 24 q^{47} - 28 q^{48} - 528 q^{49} + 72 q^{56} - 4 q^{58} - 12 q^{59} - 48 q^{60} - 16 q^{64} - 28 q^{66} - 4 q^{67} + 4 q^{69} - 32 q^{70} - 40 q^{75} - 6 q^{77} + 88 q^{78} - 16 q^{81} - 32 q^{82} - 12 q^{86} + 22 q^{88} + 40 q^{91} + 216 q^{92} + 4 q^{93} - 8 q^{97} + 46 q^{99} + O(q^{100}) \)

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.