Properties

Label 2736.2.ha
Level $2736$
Weight $2$
Character orbit 2736.ha
Rep. character $\chi_{2736}(253,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2376$
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.ha (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5856 2424 3432
Cusp forms 5664 2376 3288
Eisenstein series 192 48 144

Trace form

\( 2376q + 12q^{2} - 12q^{4} + 12q^{5} + 6q^{8} + O(q^{10}) \) \( 2376q + 12q^{2} - 12q^{4} + 12q^{5} + 6q^{8} - 42q^{10} + 6q^{11} - 12q^{13} + 24q^{14} + 24q^{17} - 12q^{19} + 24q^{20} - 12q^{22} + 54q^{26} - 36q^{28} + 12q^{29} + 60q^{31} - 18q^{32} - 72q^{34} + 42q^{35} - 24q^{37} + 126q^{38} + 18q^{40} - 12q^{43} - 54q^{44} + 24q^{46} + 24q^{47} + 1104q^{49} - 12q^{50} - 60q^{52} + 12q^{53} + 108q^{56} - 24q^{58} + 12q^{59} - 12q^{61} - 6q^{64} + 12q^{65} - 12q^{67} + 42q^{68} - 126q^{70} + 96q^{74} + 36q^{76} + 108q^{77} - 24q^{79} + 72q^{80} + 48q^{82} + 6q^{83} - 108q^{85} + 12q^{86} - 6q^{88} - 54q^{91} + 12q^{92} + 60q^{94} + 24q^{95} - 24q^{97} + 84q^{98} + O(q^{100}) \)

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

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