Properties

Label 810.3.u
Level $810$
Weight $3$
Character orbit 810.u
Rep. character $\chi_{810}(11,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1296$
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.u (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(486\)

Dimensions

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

Total New Old
Modular forms 5904 1296 4608
Cusp forms 5760 1296 4464
Eisenstein series 144 0 144

Trace form

\( 1296 q + O(q^{10}) \) \( 1296 q - 144 q^{18} - 324 q^{23} + 108 q^{27} + 324 q^{29} + 756 q^{33} + 216 q^{38} - 216 q^{41} - 648 q^{47} - 36 q^{51} + 432 q^{57} + 108 q^{59} + 1080 q^{63} + 1080 q^{65} + 2016 q^{66} + 432 q^{68} + 1872 q^{69} - 540 q^{70} + 2592 q^{71} + 864 q^{74} - 216 q^{76} + 576 q^{78} - 108 q^{79} - 288 q^{81} - 864 q^{83} - 144 q^{84} + 540 q^{85} - 1728 q^{86} + 432 q^{88} - 324 q^{89} - 1440 q^{90} - 3744 q^{93} + 756 q^{94} - 2160 q^{95} - 576 q^{96} - 2592 q^{98} - 2232 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)