Properties

Label 1045.6.cn
Level $1045$
Weight $6$
Character orbit 1045.cn
Rep. character $\chi_{1045}(29,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $14304$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.cn (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 14496 14496 0
Cusp forms 14304 14304 0
Eisenstein series 192 192 0

Trace form

\( 14304 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} + O(q^{10}) \) \( 14304 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} + 450 q^{11} + 7500 q^{14} + 2358 q^{15} + 348 q^{16} - 60 q^{19} + 39102 q^{20} + 900 q^{24} + 34830 q^{25} - 18 q^{26} - 60 q^{29} - 15 q^{30} - 54 q^{31} - 96 q^{34} - 30 q^{35} + 3570 q^{36} - 120 q^{39} - 126240 q^{40} - 108510 q^{41} - 7632 q^{44} - 63978 q^{45} - 90 q^{46} + 4061688 q^{49} - 45 q^{50} - 60 q^{51} + 235284 q^{55} - 172296 q^{59} + 139047 q^{60} - 60 q^{61} - 6979602 q^{64} + 2203104 q^{66} - 54 q^{69} - 59847 q^{70} - 325020 q^{71} - 60 q^{74} - 60 q^{79} - 332970 q^{80} + 72024 q^{81} - 90 q^{84} - 1944090 q^{85} - 94296 q^{86} + 431544 q^{89} - 768990 q^{90} - 187530 q^{91} - 767880 q^{95} + 5844360 q^{96} - 1686216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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