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Properties

Label 1368.2.eg
Level $1368$
Weight $2$
Character orbit 1368.eg
Rep. character $\chi_{1368}(91,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $588$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.eg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 1488 612 876
Cusp forms 1392 588 804
Eisenstein series 96 24 72

Trace form

\( 588 q + 6 q^{2} + 9 q^{8} + O(q^{10}) \) \( 588 q + 6 q^{2} + 9 q^{8} + 9 q^{10} + 6 q^{11} + 3 q^{14} - 12 q^{16} + 12 q^{17} - 12 q^{19} + 42 q^{20} - 12 q^{25} - 21 q^{26} - 36 q^{28} - 39 q^{32} + 36 q^{34} + 42 q^{35} + 54 q^{38} - 48 q^{40} + 24 q^{41} - 12 q^{43} - 69 q^{44} + 36 q^{46} + 252 q^{49} + 36 q^{50} + 3 q^{52} + 60 q^{58} + 12 q^{59} + 66 q^{62} + 27 q^{64} + 18 q^{65} - 12 q^{67} + 6 q^{68} - 135 q^{70} + 12 q^{73} + 87 q^{74} - 78 q^{76} + 63 q^{80} - 33 q^{82} + 6 q^{83} + 132 q^{86} - 81 q^{88} + 12 q^{89} - 54 q^{91} + 48 q^{92} - 12 q^{97} + 51 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

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