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Properties

Label 2736.3.ba
Level $2736$
Weight $3$
Character orbit 2736.ba
Rep. character $\chi_{2736}(1027,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $720$
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.ba (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1936 720 1216
Cusp forms 1904 720 1184
Eisenstein series 32 0 32

Trace form

\( 720 q + 12 q^{4} + O(q^{10}) \) \( 720 q + 12 q^{4} + 32 q^{11} - 44 q^{14} + 4 q^{16} + 80 q^{20} - 172 q^{22} - 128 q^{23} + 48 q^{26} + 120 q^{28} + 32 q^{29} + 180 q^{32} - 160 q^{34} - 96 q^{37} + 264 q^{40} - 32 q^{43} + 228 q^{44} + 5040 q^{49} - 16 q^{50} + 580 q^{52} - 160 q^{53} + 512 q^{55} - 196 q^{56} - 480 q^{58} + 160 q^{59} - 444 q^{62} - 32 q^{65} + 32 q^{67} - 96 q^{68} - 564 q^{70} + 512 q^{71} + 88 q^{74} + 224 q^{77} + 1088 q^{80} + 124 q^{82} + 480 q^{83} + 1372 q^{86} + 296 q^{88} - 192 q^{91} + 592 q^{92} + 744 q^{94} - 304 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)