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Properties

Label 1368.2.dn
Level $1368$
Weight $2$
Character orbit 1368.dn
Rep. character $\chi_{1368}(41,\cdot)$
Character field $\Q(\zeta_{18})$
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.dn (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 360 1128
Cusp forms 1392 360 1032
Eisenstein series 96 0 96

Trace form

\( 360 q + 6 q^{3} + 18 q^{9} + O(q^{10}) \) \( 360 q + 6 q^{3} + 18 q^{9} - 12 q^{15} - 36 q^{23} + 9 q^{27} - 36 q^{33} - 18 q^{39} - 18 q^{43} + 18 q^{45} - 180 q^{49} + 18 q^{51} - 48 q^{57} + 54 q^{63} - 18 q^{67} + 54 q^{73} - 6 q^{81} - 18 q^{87} + 54 q^{89} - 36 q^{91} + 54 q^{93} - 162 q^{95} + 54 q^{97} + 21 q^{99} + O(q^{100}) \)

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

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