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Properties

Label 2736.2.r
Level $2736$
Weight $2$
Character orbit 2736.r
Rep. character $\chi_{2736}(49,\cdot)$
Character field $\Q(\zeta_{3})$
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.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 236 q + q^{3} + q^{5} + 2 q^{7} - 5 q^{9} + O(q^{10}) \) \( 236 q + q^{3} + q^{5} + 2 q^{7} - 5 q^{9} + 2 q^{11} - 2 q^{13} - 5 q^{15} + 2 q^{17} + 4 q^{19} - 4 q^{21} + 2 q^{23} - 109 q^{25} + 4 q^{27} + q^{29} - 4 q^{31} - 4 q^{33} - 3 q^{35} - 8 q^{37} + 7 q^{39} + 3 q^{41} + 14 q^{43} - 9 q^{45} - q^{47} - 108 q^{49} - 5 q^{51} - 2 q^{53} - 3 q^{55} - 7 q^{57} + 35 q^{59} + q^{61} - 31 q^{63} - 20 q^{65} + 2 q^{67} - 7 q^{69} - 26 q^{71} - 8 q^{73} + 50 q^{75} + 26 q^{77} + 2 q^{79} - 13 q^{81} + 2 q^{83} + 18 q^{85} + 21 q^{87} - 10 q^{89} - 11 q^{91} + 5 q^{93} - 27 q^{95} + 10 q^{97} - 33 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \)