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Properties

Label 531.8.j
Level $531$
Weight $8$
Character orbit 531.j
Rep. character $\chi_{531}(8,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $3920$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 531.j (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(531, [\chi])\).

Total New Old
Modular forms 11872 3920 7952
Cusp forms 11648 3920 7728
Eisenstein series 224 0 224

Trace form

\( 3920 q - 8960 q^{4} + 2696 q^{7} + O(q^{10}) \) \( 3920 q - 8960 q^{4} + 2696 q^{7} - 574576 q^{16} - 131344 q^{22} + 2248964 q^{25} + 1074016 q^{28} - 4096416 q^{46} - 16084820 q^{49} - 44903856 q^{64} - 12458592 q^{76} + 10083936 q^{79} - 4498728 q^{85} - 41978968 q^{88} + 35475904 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)