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Properties

Label 1296.3.bc
Level $1296$
Weight $3$
Character orbit 1296.bc
Rep. character $\chi_{1296}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $210$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.bc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 2700 222 2478
Cusp forms 2484 210 2274
Eisenstein series 216 12 204

Trace form

\( 210 q + 6 q^{5} + 6 q^{7} + O(q^{10}) \) \( 210 q + 6 q^{5} + 6 q^{7} - 6 q^{11} - 6 q^{13} + 9 q^{17} + 3 q^{19} - 6 q^{23} - 6 q^{25} - 66 q^{29} + 6 q^{31} - 9 q^{35} - 3 q^{37} - 30 q^{41} + 6 q^{43} - 222 q^{47} - 6 q^{49} + 12 q^{55} - 222 q^{59} - 6 q^{61} - 138 q^{65} + 6 q^{67} - 9 q^{71} - 3 q^{73} + 150 q^{77} + 6 q^{79} + 354 q^{83} - 81 q^{85} + 333 q^{89} + 3 q^{91} - 1227 q^{95} + 174 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)