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Properties

Label 1584.2.r
Level $1584$
Weight $2$
Character orbit 1584.r
Rep. character $\chi_{1584}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $236$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 244 348
Cusp forms 560 236 324
Eisenstein series 32 8 24

Trace form

\( 236 q + 4 q^{5} + O(q^{10}) \) \( 236 q + 4 q^{5} - 2 q^{11} - 16 q^{14} - 8 q^{16} + 12 q^{20} + 4 q^{22} - 8 q^{23} + 56 q^{26} - 16 q^{34} - 20 q^{37} - 24 q^{38} - 4 q^{44} - 220 q^{49} + 20 q^{53} + 28 q^{55} - 16 q^{56} - 8 q^{58} - 12 q^{59} - 24 q^{64} + 4 q^{67} + 40 q^{70} - 24 q^{71} - 20 q^{77} + 96 q^{80} - 32 q^{82} - 24 q^{86} - 40 q^{91} + 132 q^{92} - 8 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)