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Properties

Label 810.4.m
Level $810$
Weight $4$
Character orbit 810.m
Rep. character $\chi_{810}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.m (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 2040 288 1752
Cusp forms 1848 288 1560
Eisenstein series 192 0 192

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 2304 q^{16} - 576 q^{25} + 576 q^{37} - 2016 q^{46} + 3168 q^{55} + 2520 q^{58} + 72 q^{61} + 2448 q^{67} - 1872 q^{82} - 828 q^{85} + 4032 q^{91} + 4212 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)