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Properties

Label 1296.3.bo
Level $1296$
Weight $3$
Character orbit 1296.bo
Rep. character $\chi_{1296}(65,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $1926$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.bo (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1296, [\chi])\).

Total New Old
Modular forms 7884 1962 5922
Cusp forms 7668 1926 5742
Eisenstein series 216 36 180

Trace form

\( 1926 q + 18 q^{3} - 18 q^{5} + 18 q^{7} - 18 q^{9} + O(q^{10}) \) \( 1926 q + 18 q^{3} - 18 q^{5} + 18 q^{7} - 18 q^{9} + 18 q^{11} - 18 q^{13} + 18 q^{15} - 18 q^{17} + 18 q^{19} - 18 q^{21} + 18 q^{23} - 18 q^{25} + 18 q^{27} - 18 q^{29} + 18 q^{31} - 18 q^{33} + 18 q^{35} - 18 q^{37} + 18 q^{39} - 18 q^{41} + 18 q^{43} - 18 q^{45} + 18 q^{47} - 18 q^{49} + 18 q^{51} - 27 q^{53} + 9 q^{55} - 18 q^{57} + 18 q^{59} - 18 q^{61} + 18 q^{63} - 18 q^{65} + 18 q^{67} - 18 q^{69} + 18 q^{71} - 18 q^{73} + 18 q^{75} - 18 q^{77} + 18 q^{79} - 18 q^{81} + 18 q^{83} - 18 q^{85} + 18 q^{87} + 306 q^{89} + 18 q^{91} - 18 q^{93} - 1926 q^{95} - 18 q^{97} - 1278 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)