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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

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

Display 100 coefficients 10 coefficients

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

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