Properties

Label 810.4.s
Level $810$
Weight $4$
Character orbit 810.s
Rep. character $\chi_{810}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $648$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 810.s (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(810, [\chi])\).

Total New Old
Modular forms 5976 648 5328
Cusp forms 5688 648 5040
Eisenstein series 288 0 288

Trace form

\( 648 q + 48 q^{11} + 384 q^{20} - 312 q^{23} - 864 q^{25} + 4968 q^{35} - 72 q^{38} + 936 q^{41} - 3444 q^{47} - 672 q^{50} + 1056 q^{56} + 108 q^{61} + 696 q^{65} - 7344 q^{67} + 1152 q^{68} - 9840 q^{77}+ \cdots - 13824 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)