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Properties

Label 2736.2.fb
Level $2736$
Weight $2$
Character orbit 2736.fb
Rep. character $\chi_{2736}(401,\cdot)$
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.fb (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

\( 708 q + 6 q^{3} - 9 q^{5} - 3 q^{7} + 6 q^{9} + O(q^{10}) \) \( 708 q + 6 q^{3} - 9 q^{5} - 3 q^{7} + 6 q^{9} - 3 q^{13} + 6 q^{15} + 12 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{25} + 9 q^{27} - 9 q^{29} - 45 q^{35} + 12 q^{39} - 9 q^{41} + 21 q^{43} - 3 q^{45} + 9 q^{47} - 315 q^{49} + 6 q^{51} - 3 q^{55} - 6 q^{57} + 9 q^{59} - 3 q^{61} - 69 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{69} + 24 q^{73} - 18 q^{77} + 3 q^{79} - 18 q^{81} + 9 q^{83} - 3 q^{85} + 3 q^{87} + 69 q^{91} + 12 q^{93} + 171 q^{95} + 33 q^{97} - 48 q^{99} + O(q^{100}) \)

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

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