↑

Properties

Label 825.6.r
Level $825$
Weight $6$
Character orbit 825.r
Rep. character $\chi_{825}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1200$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 825.r (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(825, [\chi])\).

Total New Old
Modular forms 2416 1200 1216
Cusp forms 2384 1200 1184
Eisenstein series 32 0 32

Trace form

\( 1200 q + 19200 q^{4} - 44 q^{5} - 144 q^{6} - 156 q^{7} - 24300 q^{9} + O(q^{10}) \) \( 1200 q + 19200 q^{4} - 44 q^{5} - 144 q^{6} - 156 q^{7} - 24300 q^{9} - 1312 q^{10} + 316 q^{11} - 396 q^{12} + 1572 q^{13} + 792 q^{15} + 299544 q^{16} + 382 q^{17} + 26616 q^{19} - 9636 q^{20} - 3528 q^{21} + 3620 q^{22} + 10208 q^{23} - 6912 q^{24} + 352 q^{25} - 6490 q^{26} - 9376 q^{28} + 6984 q^{30} + 3322 q^{31} - 76740 q^{32} + 15624 q^{33} + 29918 q^{35} - 388800 q^{36} - 3850 q^{37} - 74536 q^{38} - 24336 q^{39} - 53304 q^{40} + 18456 q^{41} + 8712 q^{42} - 22128 q^{43} + 40916 q^{44} + 5346 q^{45} - 40592 q^{46} + 82786 q^{47} - 12672 q^{48} - 735392 q^{49} - 88374 q^{50} - 41616 q^{51} + 22192 q^{52} - 63624 q^{53} - 11664 q^{54} - 10576 q^{55} - 31212 q^{57} + 150192 q^{58} + 7656 q^{59} + 19620 q^{60} - 63878 q^{61} + 173950 q^{62} - 12636 q^{63} + 4672104 q^{64} - 93134 q^{65} - 83448 q^{66} + 27244 q^{67} + 425174 q^{68} - 70488 q^{69} + 401946 q^{70} + 203016 q^{71} - 2566 q^{73} + 12122 q^{74} - 13572 q^{75} + 1454988 q^{76} + 151934 q^{77} + 151416 q^{78} - 264558 q^{79} - 884552 q^{80} - 1968300 q^{81} + 750156 q^{82} + 139204 q^{83} - 169344 q^{84} - 453694 q^{85} + 340552 q^{86} + 73080 q^{87} + 371436 q^{88} + 109188 q^{90} + 129190 q^{91} + 636890 q^{92} - 7128 q^{93} - 49724 q^{94} + 361020 q^{95} - 258048 q^{96} - 551650 q^{97} + 36616 q^{98} - 38394 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)