Properties

Label 2736.2.ck
Level $2736$
Weight $2$
Character orbit 2736.ck
Rep. character $\chi_{2736}(977,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $236$
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.ck (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 984 244 740
Cusp forms 936 236 700
Eisenstein series 48 8 40

Trace form

\( 236q + 3q^{3} - 3q^{5} + 2q^{7} - 5q^{9} + O(q^{10}) \) \( 236q + 3q^{3} - 3q^{5} + 2q^{7} - 5q^{9} + 6q^{11} + 3q^{15} - 12q^{17} + 4q^{19} + 6q^{21} + 111q^{25} - 3q^{29} - 18q^{31} - 12q^{33} + 15q^{35} + q^{39} + 3q^{41} + 14q^{43} + q^{45} + 3q^{47} - 108q^{49} + 3q^{51} + 7q^{55} - 17q^{57} + 3q^{59} + q^{61} + 5q^{63} - 24q^{65} + 9q^{69} + 4q^{73} + 60q^{75} - 6q^{77} - 13q^{81} + 6q^{83} - 22q^{85} + 21q^{87} + 3q^{91} - 7q^{93} - 51q^{95} + 35q^{99} + O(q^{100}) \)

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

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