Properties

Label 2736.2.gk
Level $2736$
Weight $2$
Character orbit 2736.gk
Rep. character $\chi_{2736}(257,\cdot)$
Character field $\Q(\zeta_{18})$
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.gk (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 708q + 6q^{3} - 9q^{5} + 6q^{7} - 12q^{9} + O(q^{10}) \) \( 708q + 6q^{3} - 9q^{5} + 6q^{7} - 12q^{9} + 9q^{11} - 3q^{13} + 6q^{15} + 12q^{19} - 24q^{21} + 9q^{23} - 3q^{25} + 9q^{27} - 9q^{29} + 9q^{31} - 9q^{33} + 45q^{35} + 12q^{39} - 27q^{41} - 33q^{43} - 3q^{45} + 9q^{47} + 630q^{49} + 6q^{51} - 3q^{55} - 6q^{57} + 9q^{59} - 3q^{61} + 156q^{63} - 9q^{65} + 3q^{67} - 9q^{69} + 24q^{73} - 18q^{77} + 3q^{79} - 3q^{85} + 3q^{87} + 69q^{91} - 15q^{93} + 9q^{95} - 21q^{97} + 33q^{99} + O(q^{100}) \)

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

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