↑

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 $960$

Related objects

Downloads

Learn more

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

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

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

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