Properties

Label 1368.2.q
Level $1368$
Weight $2$
Character orbit 1368.q
Rep. character $\chi_{1368}(457,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $108$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 496 108 388
Cusp forms 464 108 356
Eisenstein series 32 0 32

Trace form

\( 108 q - 4 q^{5} - 4 q^{9} + O(q^{10}) \) \( 108 q - 4 q^{5} - 4 q^{9} + 12 q^{11} + 12 q^{15} + 16 q^{17} + 24 q^{21} - 54 q^{25} - 36 q^{27} - 12 q^{29} - 8 q^{33} - 72 q^{35} - 54 q^{39} + 4 q^{41} - 12 q^{45} - 6 q^{47} - 42 q^{49} + 12 q^{51} + 8 q^{53} + 24 q^{55} + 12 q^{61} - 4 q^{63} - 16 q^{69} + 16 q^{71} + 16 q^{75} - 40 q^{77} - 12 q^{79} - 12 q^{81} + 56 q^{83} - 24 q^{85} + 14 q^{87} + 24 q^{89} - 16 q^{93} - 24 q^{97} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)