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Properties

Label 825.4.o
Level $825$
Weight $4$
Character orbit 825.o
Rep. character $\chi_{825}(421,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $720$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.o (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

\( 720 q - 720 q^{4} - 24 q^{5} - 96 q^{6} - 22 q^{7} - 1620 q^{9} + O(q^{10}) \) \( 720 q - 720 q^{4} - 24 q^{5} - 96 q^{6} - 22 q^{7} - 1620 q^{9} - 132 q^{10} - 56 q^{11} - 12 q^{12} + 96 q^{13} + 90 q^{15} - 2844 q^{16} + 384 q^{17} + 256 q^{19} - 4 q^{20} + 168 q^{21} + 200 q^{22} - 56 q^{23} + 288 q^{24} + 804 q^{25} + 40 q^{26} - 328 q^{28} + 564 q^{30} + 138 q^{31} - 680 q^{32} - 228 q^{33} - 1420 q^{35} + 25920 q^{36} - 360 q^{37} - 3108 q^{38} + 624 q^{39} + 2928 q^{40} - 96 q^{41} + 204 q^{42} - 2424 q^{43} - 1694 q^{44} + 144 q^{45} - 3808 q^{46} - 1368 q^{47} - 96 q^{48} - 8322 q^{49} - 918 q^{50} + 816 q^{51} - 336 q^{52} + 1248 q^{53} + 216 q^{54} - 440 q^{55} + 156 q^{57} - 3004 q^{58} + 816 q^{59} - 12 q^{60} + 8 q^{61} - 1560 q^{62} + 252 q^{63} - 10296 q^{64} - 3780 q^{65} - 1272 q^{66} + 3128 q^{67} - 1118 q^{68} + 312 q^{69} + 1196 q^{70} - 136 q^{71} - 3528 q^{73} - 1078 q^{74} - 720 q^{75} - 16968 q^{76} + 4488 q^{77} - 72 q^{78} - 12388 q^{79} + 4682 q^{80} - 14580 q^{81} + 8672 q^{82} - 1088 q^{83} - 8064 q^{84} - 860 q^{85} - 3492 q^{86} + 3300 q^{87} - 4132 q^{88} + 972 q^{90} + 1020 q^{91} - 6720 q^{92} - 4104 q^{93} - 18264 q^{94} - 3952 q^{95} + 2688 q^{96} + 1800 q^{97} + 508 q^{98} - 504 q^{99} + O(q^{100}) \)

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

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