Properties

Label 2736.2.do
Level $2736$
Weight $2$
Character orbit 2736.do
Rep. character $\chi_{2736}(1189,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $792$
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.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 1952 808 1144
Cusp forms 1888 792 1096
Eisenstein series 64 16 48

Trace form

\( 792q + 2q^{2} - 2q^{4} + 2q^{5} - 4q^{8} + O(q^{10}) \) \( 792q + 2q^{2} - 2q^{4} + 2q^{5} - 4q^{8} + 8q^{10} + 8q^{11} - 2q^{13} - 2q^{14} - 6q^{16} + 4q^{17} + 4q^{19} + 36q^{20} - 2q^{22} - 4q^{26} + 26q^{28} + 2q^{29} - 64q^{31} + 32q^{32} + 4q^{34} + 16q^{35} - 8q^{37} - 2q^{38} - 12q^{40} - 2q^{43} - 4q^{44} - 24q^{46} + 4q^{47} - 760q^{49} - 28q^{50} + 14q^{52} + 2q^{53} - 116q^{56} - 36q^{58} + 2q^{59} - 34q^{61} + 62q^{62} - 44q^{64} + 16q^{65} - 26q^{67} - 24q^{68} + 24q^{70} - 46q^{74} - 18q^{76} - 48q^{77} - 76q^{79} - 22q^{80} + 10q^{82} - 32q^{83} + 2q^{85} + 34q^{86} - 68q^{88} + 12q^{91} + 6q^{92} - 136q^{94} - 16q^{95} - 4q^{97} - 78q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)