↑

Properties

Label 1368.3.eh
Level $1368$
Weight $3$
Character orbit 1368.eh
Rep. character $\chi_{1368}(595,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1188$
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.eh (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2928 1212 1716
Cusp forms 2832 1188 1644
Eisenstein series 96 24 72

Trace form

\( 1188 q + 6 q^{2} + 3 q^{8} + O(q^{10}) \) \( 1188 q + 6 q^{2} + 3 q^{8} + 51 q^{10} + 6 q^{11} + 63 q^{14} + 36 q^{16} + 12 q^{17} - 12 q^{19} - 18 q^{20} + 6 q^{22} - 12 q^{25} - 69 q^{26} + 108 q^{28} + 51 q^{32} - 84 q^{34} + 162 q^{35} + 54 q^{38} - 72 q^{40} - 60 q^{41} - 12 q^{43} - 153 q^{44} + 132 q^{46} + 3900 q^{49} + 120 q^{50} - 261 q^{52} + 306 q^{56} - 84 q^{58} + 12 q^{59} - 432 q^{62} - 81 q^{64} + 6 q^{65} - 12 q^{67} - 54 q^{68} - 45 q^{70} - 252 q^{73} + 123 q^{74} - 54 q^{76} + 3 q^{80} - 15 q^{82} + 6 q^{83} + 780 q^{86} + 69 q^{88} + 12 q^{89} - 306 q^{91} + 1104 q^{92} + 162 q^{94} - 12 q^{97} - 867 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)