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Properties

Label 2736.3.ep
Level $2736$
Weight $3$
Character orbit 2736.ep
Rep. character $\chi_{2736}(163,\cdot)$
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.ep (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

\( 1592 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 16 q^{7} - 4 q^{8} + O(q^{10}) \) \( 1592 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 16 q^{7} - 4 q^{8} - 4 q^{10} + 8 q^{11} - 2 q^{13} + 10 q^{14} + 26 q^{16} + 4 q^{17} + 28 q^{19} - 76 q^{20} - 2 q^{22} + 4 q^{23} - 188 q^{26} - 94 q^{28} + 2 q^{29} - 48 q^{32} + 72 q^{34} + 148 q^{35} - 8 q^{37} - 38 q^{38} - 92 q^{40} - 2 q^{43} - 204 q^{44} - 432 q^{46} + 10792 q^{49} + 116 q^{50} + 78 q^{52} + 2 q^{53} - 4 q^{55} + 12 q^{56} - 92 q^{58} + 2 q^{59} + 62 q^{61} - 414 q^{62} - 236 q^{64} + 16 q^{65} + 286 q^{67} - 744 q^{68} + 80 q^{70} + 4 q^{71} + 178 q^{74} + 374 q^{76} + 400 q^{77} + 426 q^{80} - 278 q^{82} - 152 q^{83} + 258 q^{85} + 226 q^{86} + 572 q^{88} - 100 q^{91} + 70 q^{92} - 528 q^{94} - 4 q^{97} + 314 q^{98} + O(q^{100}) \)

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

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