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Properties

Label 1368.2.de
Level $1368$
Weight $2$
Character orbit 1368.de
Rep. character $\chi_{1368}(169,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $360$
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.de (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1488 360 1128
Cusp forms 1392 360 1032
Eisenstein series 96 0 96

Trace form

\( 360 q + 3 q^{3} - 9 q^{9} + O(q^{10}) \) \( 360 q + 3 q^{3} - 9 q^{9} + 12 q^{15} + 24 q^{23} - 3 q^{27} + 9 q^{33} + 18 q^{39} + 9 q^{41} + 36 q^{43} - 18 q^{45} + 360 q^{49} + 24 q^{51} + 24 q^{57} - 21 q^{59} + 108 q^{63} + 48 q^{65} - 9 q^{67} - 54 q^{73} + 15 q^{81} - 36 q^{87} - 18 q^{89} + 36 q^{91} - 84 q^{95} + 27 q^{97} + 21 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)