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

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

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

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