Properties

Label 1584.2.cq
Level $1584$
Weight $2$
Character orbit 1584.cq
Rep. character $\chi_{1584}(179,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $768$
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.cq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2368 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 16 q^{16} - 80 q^{22} + 48 q^{28} + 64 q^{43} - 64 q^{46} - 192 q^{49} + 32 q^{52} + 64 q^{55} + 16 q^{58} - 144 q^{64} + 32 q^{67} + 48 q^{70} + 256 q^{76} + 120 q^{82} + 32 q^{88} + 144 q^{91} + 192 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)