↑

Properties

Label 1368.3.co
Level $1368$
Weight $3$
Character orbit 1368.co
Rep. character $\chi_{1368}(115,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $864$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.co (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 968 864 104
Cusp forms 952 864 88
Eisenstein series 16 0 16

Trace form

\( 864 q + 6 q^{6} - 36 q^{8} + O(q^{10}) \) \( 864 q + 6 q^{6} - 36 q^{8} + 70 q^{12} - 30 q^{14} + 92 q^{18} - 148 q^{24} + 2160 q^{25} + 168 q^{26} + 96 q^{27} + 100 q^{30} - 120 q^{32} - 90 q^{36} - 60 q^{42} - 288 q^{44} - 182 q^{48} + 3024 q^{49} - 282 q^{50} - 160 q^{51} - 18 q^{52} - 228 q^{54} + 84 q^{56} - 90 q^{58} + 288 q^{59} - 186 q^{60} + 252 q^{64} - 338 q^{66} + 540 q^{68} + 600 q^{72} - 504 q^{74} - 68 q^{78} + 1092 q^{80} + 32 q^{81} - 396 q^{82} - 480 q^{83} + 858 q^{84} + 768 q^{86} - 24 q^{88} + 192 q^{89} + 350 q^{90} - 114 q^{92} + 114 q^{94} + 876 q^{96} + 1368 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)