Properties

Label 648.4.y
Level $648$
Weight $4$
Character orbit 648.y
Rep. character $\chi_{648}(25,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1458$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.y (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(648, [\chi])\).

Total New Old
Modular forms 5904 1458 4446
Cusp forms 5760 1458 4302
Eisenstein series 144 0 144

Trace form

\( 1458q + O(q^{10}) \) \( 1458q + 1854q^{41} + 1026q^{45} - 594q^{47} - 2961q^{51} - 2862q^{53} - 2214q^{57} - 1449q^{59} + 1998q^{63} + 4266q^{65} + 3366q^{69} - 6345q^{89} - 5562q^{93} - 7938q^{95} + 5670q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)