Properties

Label 2736.2.dl
Level $2736$
Weight $2$
Character orbit 2736.dl
Rep. character $\chi_{2736}(625,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $708$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.dl (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 2952 732 2220
Cusp forms 2808 708 2100
Eisenstein series 144 24 120

Trace form

\( 708q + 6q^{3} - 3q^{5} - 3q^{7} + 6q^{9} + O(q^{10}) \) \( 708q + 6q^{3} - 3q^{5} - 3q^{7} + 6q^{9} + 6q^{11} - 3q^{13} + 6q^{15} - 12q^{17} + 12q^{19} + 3q^{21} + 3q^{23} - 3q^{25} + 3q^{27} - 3q^{29} + 6q^{31} - 12q^{33} + 27q^{35} - 24q^{37} + 12q^{39} + 9q^{41} + 21q^{43} - 3q^{45} + 3q^{47} - 315q^{49} + 6q^{51} - 12q^{53} + 27q^{55} - 6q^{57} + 3q^{59} - 3q^{61} + 39q^{63} - 6q^{65} + 3q^{67} - 3q^{69} + 12q^{71} - 48q^{73} - 72q^{75} - 48q^{77} + 3q^{79} - 18q^{81} - 3q^{83} - 3q^{85} + 3q^{87} - 12q^{89} - 3q^{91} - 24q^{93} - 51q^{95} - 39q^{97} + 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

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