↑

Properties

Label 825.4.m
Level $825$
Weight $4$
Character orbit 825.m
Rep. character $\chi_{825}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $720$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(825, [\chi])\).

Total New Old
Modular forms 1456 720 736
Cusp forms 1424 720 704
Eisenstein series 32 0 32

Trace form

\( 720 q - 720 q^{4} + 16 q^{5} + 24 q^{6} - 22 q^{7} - 1620 q^{9} + O(q^{10}) \) \( 720 q - 720 q^{4} + 16 q^{5} + 24 q^{6} - 22 q^{7} - 1620 q^{9} - 132 q^{10} - 56 q^{11} - 12 q^{12} - 144 q^{13} - 60 q^{15} - 2844 q^{16} + 64 q^{17} + 316 q^{19} - 314 q^{20} + 168 q^{21} + 440 q^{22} - 56 q^{23} + 288 q^{24} - 386 q^{25} + 40 q^{26} - 48 q^{28} - 456 q^{30} + 828 q^{31} - 680 q^{32} + 342 q^{33} - 400 q^{35} - 6480 q^{36} + 240 q^{37} + 2072 q^{38} + 624 q^{39} - 2482 q^{40} + 384 q^{41} + 1224 q^{42} - 2424 q^{43} - 364 q^{44} + 144 q^{45} + 952 q^{46} + 2852 q^{47} + 384 q^{48} - 8322 q^{49} + 4822 q^{50} + 816 q^{51} + 2004 q^{52} - 312 q^{53} + 216 q^{54} - 380 q^{55} + 156 q^{57} + 1186 q^{58} - 204 q^{59} - 972 q^{60} + 2368 q^{61} + 390 q^{62} - 108 q^{63} - 12636 q^{64} - 3780 q^{65} + 1908 q^{66} + 3128 q^{67} - 1118 q^{68} - 1248 q^{69} - 3774 q^{70} + 544 q^{71} - 1128 q^{73} - 1078 q^{74} - 840 q^{75} - 16968 q^{76} - 12652 q^{77} - 72 q^{78} + 2992 q^{79} - 8248 q^{80} - 14580 q^{81} + 8672 q^{82} + 8112 q^{83} + 2016 q^{84} + 5420 q^{85} + 1768 q^{86} + 3300 q^{87} + 1068 q^{88} + 432 q^{90} - 3360 q^{91} - 1170 q^{92} - 4104 q^{93} + 4566 q^{94} - 272 q^{95} + 2688 q^{96} - 1830 q^{97} + 508 q^{98} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)