Properties

Label 2736.3.cq
Level $2736$
Weight $3$
Character orbit 2736.cq
Rep. character $\chi_{2736}(1265,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $476$
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.cq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1944 484 1460
Cusp forms 1896 476 1420
Eisenstein series 48 8 40

Trace form

\( 476q + q^{3} - 3q^{5} + 2q^{7} + 7q^{9} + O(q^{10}) \) \( 476q + q^{3} - 3q^{5} + 2q^{7} + 7q^{9} + 6q^{11} - 2q^{13} + 19q^{15} + 72q^{17} + 4q^{19} - 10q^{21} + 1151q^{25} + 4q^{27} - 3q^{29} + 26q^{31} - 40q^{33} + 75q^{35} - 8q^{37} + 13q^{39} - 39q^{41} + 98q^{43} + 21q^{45} + 3q^{47} - 1584q^{49} + 19q^{51} + 27q^{55} + 71q^{57} + 3q^{59} + q^{61} - 169q^{63} + 138q^{65} + 2q^{67} + 5q^{69} - 14q^{73} + 356q^{75} - 6q^{77} + 2q^{79} - 217q^{81} + 6q^{83} - 102q^{85} - 117q^{87} + 49q^{91} + 17q^{93} + 651q^{95} - 122q^{97} + 99q^{99} + O(q^{100}) \)

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

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