Properties

Label 2736.3.gj
Level $2736$
Weight $3$
Character orbit 2736.gj
Rep. character $\chi_{2736}(929,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1428$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.gj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 5832 1452 4380
Cusp forms 5688 1428 4260
Eisenstein series 144 24 120

Trace form

\( 1428q + 6q^{3} - 9q^{5} + 6q^{7} + 6q^{9} + O(q^{10}) \) \( 1428q + 6q^{3} - 9q^{5} + 6q^{7} + 6q^{9} + 9q^{11} - 3q^{13} + 6q^{15} + 12q^{19} - 60q^{21} + 9q^{23} - 3q^{25} + 3q^{27} - 9q^{29} - 3q^{31} - 93q^{33} + 225q^{35} - 24q^{37} + 12q^{39} + 99q^{41} - 285q^{43} - 3q^{45} + 9q^{47} + 9486q^{49} + 6q^{51} - 63q^{55} - 6q^{57} + 9q^{59} - 3q^{61} - 132q^{63} - 9q^{65} + 3q^{67} - 3q^{69} - 84q^{73} - 324q^{75} - 18q^{77} + 3q^{79} - 90q^{81} - 3q^{85} + 3q^{87} + 735q^{91} + 21q^{93} + 9q^{95} - 183q^{97} + 249q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)