Properties

Label 165.6.r
Level $165$
Weight $6$
Character orbit 165.r
Rep. character $\chi_{165}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $464$
Sturm bound $144$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(165, [\chi])\).

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

Trace form

\( 464 q + 1780 q^{4} - 10 q^{6} - 274 q^{9} + O(q^{10}) \) \( 464 q + 1780 q^{4} - 10 q^{6} - 274 q^{9} + 1018 q^{15} - 19236 q^{16} - 20 q^{19} - 330 q^{24} - 8514 q^{25} + 15460 q^{30} - 33652 q^{31} + 1472 q^{34} - 52366 q^{36} + 3790 q^{39} - 49290 q^{40} + 14968 q^{45} - 53060 q^{46} - 289192 q^{49} - 123810 q^{51} + 72284 q^{55} + 107754 q^{60} - 56920 q^{61} + 266496 q^{64} + 387930 q^{66} - 33774 q^{69} + 72264 q^{70} - 34198 q^{75} - 35920 q^{79} - 123594 q^{81} + 21500 q^{84} - 665630 q^{85} - 215280 q^{90} + 392080 q^{91} + 366380 q^{94} - 1734310 q^{96} - 787332 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.