↑

Properties

Label 825.6.ci
Level $825$
Weight $6$
Character orbit 825.ci
Rep. character $\chi_{825}(113,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4768$
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.ci (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q + 2 q^{3} - 2 q^{6} + 140 q^{7} - 320 q^{9} + O(q^{10}) \) \( 4768 q + 2 q^{3} - 2 q^{6} + 140 q^{7} - 320 q^{9} + 320 q^{10} + 1442 q^{12} - 1584 q^{13} + 1906 q^{15} - 1196056 q^{16} + 122 q^{18} - 12 q^{21} - 2760 q^{22} + 10240 q^{24} - 11728 q^{25} - 11494 q^{27} + 21428 q^{28} - 12506 q^{30} - 4 q^{31} - 13272 q^{33} - 40 q^{34} + 2046 q^{36} + 19296 q^{37} - 10 q^{39} + 39812 q^{40} - 29306 q^{42} + 46680 q^{43} - 22638 q^{45} - 4 q^{46} + 30984 q^{48} - 86020 q^{49} - 12 q^{51} + 34212 q^{52} - 197060 q^{54} + 120468 q^{55} - 168870 q^{57} + 29372 q^{58} + 306630 q^{60} - 4 q^{61} - 152414 q^{63} - 31110 q^{66} + 109828 q^{67} + 305580 q^{70} + 327582 q^{72} + 228620 q^{73} - 150766 q^{75} + 24512 q^{76} + 166500 q^{78} - 1044280 q^{79} + 88348 q^{81} + 380572 q^{82} + 77750 q^{84} - 263532 q^{85} + 88734 q^{87} - 149016 q^{88} + 749766 q^{90} - 4 q^{91} + 562962 q^{93} - 675100 q^{94} - 91266 q^{96} - 389256 q^{97} + 830570 q^{99} + O(q^{100}) \)

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.