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Properties

Label 810.3.l
Level $810$
Weight $3$
Character orbit 810.l
Rep. character $\chi_{810}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
Sturm bound $486$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(486\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(810, [\chi])\).

Total New Old
Modular forms 1392 192 1200
Cusp forms 1200 192 1008
Eisenstein series 192 0 192

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 384 q^{16} - 24 q^{25} - 336 q^{37} + 96 q^{46} + 528 q^{55} + 240 q^{58} + 192 q^{61} - 312 q^{67} + 48 q^{82} - 48 q^{85} + 672 q^{91} + 504 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

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