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Properties

Label 725.6.q
Level $725$
Weight $6$
Character orbit 725.q
Rep. character $\chi_{725}(51,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1404$
Sturm bound $450$

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Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 725.q (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(725, [\chi])\).

Total New Old
Modular forms 2292 1440 852
Cusp forms 2220 1404 816
Eisenstein series 72 36 36

Trace form

\( 1404 q + 7 q^{2} + 7 q^{3} + 3663 q^{4} + 63 q^{6} - 169 q^{7} - 1484 q^{8} + 17711 q^{9} + O(q^{10}) \) \( 1404 q + 7 q^{2} + 7 q^{3} + 3663 q^{4} + 63 q^{6} - 169 q^{7} - 1484 q^{8} + 17711 q^{9} - 2135 q^{11} + 211 q^{13} + 7 q^{14} - 56453 q^{16} - 13272 q^{18} + 7 q^{19} - 10521 q^{21} + 6144 q^{22} + 1605 q^{23} - 13849 q^{24} - 30037 q^{26} + 3997 q^{27} - 45012 q^{28} + 14531 q^{29} + 2849 q^{31} - 19110 q^{32} - 17143 q^{33} + 30355 q^{34} - 275170 q^{36} - 2037 q^{37} + 13112 q^{38} - 50505 q^{39} + 122770 q^{42} - 12327 q^{43} + 27804 q^{44} + 55447 q^{47} - 26796 q^{48} - 433081 q^{49} + 52432 q^{51} - 200704 q^{52} - 78200 q^{53} + 104154 q^{54} - 390523 q^{56} - 59386 q^{57} + 222207 q^{58} - 285140 q^{59} - 22981 q^{61} - 86317 q^{62} - 106027 q^{63} + 1080508 q^{64} + 63735 q^{66} + 22557 q^{67} - 454804 q^{68} + 25235 q^{69} + 155339 q^{71} - 845775 q^{72} + 368816 q^{73} + 92946 q^{74} - 4935 q^{76} + 485877 q^{77} - 39177 q^{78} - 296569 q^{79} - 1719757 q^{81} - 147012 q^{82} + 34495 q^{83} + 522571 q^{84} + 559584 q^{86} + 308795 q^{87} + 568366 q^{88} - 507227 q^{89} - 56109 q^{91} + 91566 q^{92} + 749741 q^{93} + 558324 q^{94} - 1689912 q^{96} + 953316 q^{97} + 97482 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(725, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(725, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(725, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)