Properties

Label 1368.3.ci
Level $1368$
Weight $3$
Character orbit 1368.ci
Rep. character $\chi_{1368}(425,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.ci (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 976 240 736
Cusp forms 944 240 704
Eisenstein series 32 0 32

Trace form

\( 240q - 4q^{3} + 12q^{9} + O(q^{10}) \) \( 240q - 4q^{3} + 12q^{9} - 18q^{11} + 8q^{15} + 108q^{17} - 6q^{19} + 600q^{25} - 40q^{27} - 24q^{31} - 72q^{33} - 52q^{39} + 54q^{41} - 216q^{43} + 160q^{45} - 108q^{47} - 840q^{49} - 14q^{51} - 4q^{57} - 126q^{59} + 20q^{63} + 432q^{65} - 84q^{67} + 16q^{69} - 18q^{73} - 214q^{75} - 288q^{77} - 92q^{81} - 124q^{87} + 216q^{89} - 96q^{91} + 144q^{93} - 468q^{95} - 180q^{97} + 170q^{99} + O(q^{100}) \)

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

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