Properties

Label 825.6.cb
Level $825$
Weight $6$
Character orbit 825.cb
Rep. character $\chi_{825}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1200$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 825.cb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 1200 q + 4800 q^{4} + 66 q^{5} - 576 q^{6} - 190 q^{7} + 24300 q^{9} + O(q^{10}) \) \( 1200 q + 4800 q^{4} + 66 q^{5} - 576 q^{6} - 190 q^{7} + 24300 q^{9} + 1348 q^{10} - 316 q^{11} + 1980 q^{12} - 75524 q^{16} - 2264 q^{19} - 11044 q^{20} + 3528 q^{21} + 2260 q^{22} - 12760 q^{23} - 6912 q^{24} + 17204 q^{25} - 25960 q^{26} - 9120 q^{28} + 10404 q^{30} - 3322 q^{31} - 14850 q^{35} + 1555200 q^{36} - 24336 q^{39} + 97448 q^{40} + 4614 q^{41} - 43560 q^{42} - 10814 q^{44} + 3564 q^{45} - 162368 q^{46} - 66440 q^{47} - 63360 q^{48} + 711698 q^{49} + 117342 q^{50} + 41616 q^{51} - 11664 q^{54} + 116110 q^{55} - 23040 q^{57} + 191460 q^{58} + 7656 q^{59} + 31068 q^{60} + 195588 q^{61} + 47790 q^{63} + 1189864 q^{64} + 167340 q^{65} + 83448 q^{66} + 171160 q^{67} + 272350 q^{68} + 17622 q^{69} + 196116 q^{70} + 47344 q^{71} + 12122 q^{74} - 159660 q^{75} - 382968 q^{76} + 136470 q^{77} + 909052 q^{79} - 458258 q^{80} - 1968300 q^{81} - 318560 q^{82} + 677376 q^{84} + 173280 q^{85} + 6588 q^{86} + 371160 q^{87} + 46400 q^{88} + 106272 q^{90} + 231570 q^{91} - 510400 q^{92} + 1315816 q^{94} - 56482 q^{95} + 258048 q^{96} - 1303540 q^{98} + 25596 q^{99} + O(q^{100}) \)

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

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