Properties

Label 525.4.n
Level $525$
Weight $4$
Character orbit 525.n
Rep. character $\chi_{525}(106,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $368$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 976 368 608
Cusp forms 944 368 576
Eisenstein series 32 0 32

Trace form

\( 368q + 8q^{2} - 384q^{4} + 16q^{5} + 96q^{8} - 828q^{9} + O(q^{10}) \) \( 368q + 8q^{2} - 384q^{4} + 16q^{5} + 96q^{8} - 828q^{9} - 32q^{10} - 48q^{12} + 192q^{13} - 24q^{15} - 1880q^{16} - 176q^{17} - 288q^{18} - 72q^{19} - 1212q^{20} - 84q^{21} + 1428q^{22} + 264q^{23} - 252q^{25} - 184q^{26} + 640q^{29} + 312q^{30} - 2904q^{32} - 576q^{33} - 456q^{34} + 56q^{35} - 3456q^{36} + 168q^{37} - 2072q^{38} - 624q^{39} - 716q^{40} + 2112q^{41} + 64q^{43} + 1596q^{44} + 144q^{45} - 1384q^{46} + 2064q^{47} - 384q^{48} + 18032q^{49} + 1188q^{50} + 3264q^{51} + 3056q^{52} - 4416q^{53} + 2968q^{55} - 72q^{57} + 584q^{58} - 816q^{59} - 996q^{60} + 2992q^{61} - 6356q^{62} - 10344q^{64} + 7336q^{65} + 2544q^{66} - 592q^{67} + 2104q^{68} + 1248q^{69} + 252q^{70} - 2128q^{71} + 864q^{72} + 432q^{73} + 2544q^{74} + 624q^{75} + 6728q^{76} + 672q^{77} + 72q^{78} - 696q^{79} - 1724q^{80} - 7452q^{81} - 16448q^{82} - 1496q^{83} - 1008q^{84} - 3696q^{85} + 7320q^{86} - 2736q^{87} - 13652q^{88} - 7536q^{89} - 288q^{90} - 1456q^{91} + 10224q^{92} + 5280q^{93} + 7132q^{94} + 7944q^{95} - 1740q^{96} + 10544q^{97} + 392q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database