↑

Properties

Label 1368.3.es
Level $1368$
Weight $3$
Character orbit 1368.es
Rep. character $\chi_{1368}(97,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.es (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 2928 720 2208
Cusp forms 2832 720 2112
Eisenstein series 96 0 96

Trace form

\( 720 q + 6 q^{3} + 18 q^{9} + O(q^{10}) \) \( 720 q + 6 q^{3} + 18 q^{9} + 24 q^{15} - 144 q^{23} + 90 q^{27} + 18 q^{33} + 36 q^{39} - 54 q^{41} + 288 q^{43} - 144 q^{45} + 5040 q^{49} - 192 q^{57} - 126 q^{59} - 432 q^{63} + 126 q^{67} + 108 q^{73} + 318 q^{81} - 504 q^{87} + 216 q^{89} + 576 q^{91} - 432 q^{93} + 864 q^{95} + 270 q^{97} - 294 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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