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Properties

Label 1368.2.x
Level $1368$
Weight $2$
Character orbit 1368.x
Rep. character $\chi_{1368}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 496 120 376
Cusp forms 464 120 344
Eisenstein series 32 0 32

Trace form

\( 120 q - 3 q^{3} + 3 q^{9} + O(q^{10}) \) \( 120 q - 3 q^{3} + 3 q^{9} - 3 q^{11} + 12 q^{15} + 18 q^{17} + 3 q^{19} + 12 q^{23} - 120 q^{25} - 18 q^{31} + 9 q^{33} - 2 q^{39} - 18 q^{41} + 12 q^{43} + 16 q^{45} - 60 q^{49} - 24 q^{51} + 29 q^{57} - 42 q^{59} + 58 q^{63} + 54 q^{65} + 9 q^{67} - 42 q^{69} + 9 q^{73} + 75 q^{75} + 24 q^{77} - 13 q^{81} - 26 q^{87} - 18 q^{89} - 18 q^{91} - 18 q^{93} + 54 q^{95} - 27 q^{97} - 4 q^{99} + O(q^{100}) \)

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

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