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Properties

Label 2736.3.dn
Level $2736$
Weight $3$
Character orbit 2736.dn
Rep. character $\chi_{2736}(829,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1592$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.dn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 3872 1608 2264
Cusp forms 3808 1592 2216
Eisenstein series 64 16 48

Trace form

\( 1592 q + 6 q^{2} - 2 q^{4} + 2 q^{5} + O(q^{10}) \) \( 1592 q + 6 q^{2} - 2 q^{4} + 2 q^{5} + 108 q^{10} + 8 q^{11} - 6 q^{13} - 18 q^{14} + 26 q^{16} + 4 q^{17} + 28 q^{19} + 92 q^{20} - 6 q^{22} - 188 q^{26} + 90 q^{28} + 6 q^{29} + 216 q^{32} + 84 q^{34} - 144 q^{35} - 234 q^{38} + 264 q^{40} - 2 q^{43} + 76 q^{44} + 4 q^{47} - 10824 q^{49} - 246 q^{52} + 6 q^{53} - 92 q^{58} + 6 q^{59} - 66 q^{61} - 414 q^{62} - 236 q^{64} - 6 q^{67} + 632 q^{68} + 792 q^{70} - 174 q^{74} - 538 q^{76} - 384 q^{77} - 12 q^{79} - 462 q^{80} - 126 q^{82} - 152 q^{83} - 62 q^{85} + 6 q^{86} + 288 q^{91} + 198 q^{92} - 376 q^{95} - 12 q^{97} - 810 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

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