Properties

Label 525.4.bm
Level $525$
Weight $4$
Character orbit 525.bm
Rep. character $\chi_{525}(131,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
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.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888q - 9q^{3} - 934q^{4} - 20q^{7} - 3q^{9} + O(q^{10}) \) \( 1888q - 9q^{3} - 934q^{4} - 20q^{7} - 3q^{9} - 60q^{10} + 39q^{12} - 506q^{15} + 3546q^{16} + 40q^{18} - 18q^{19} - 111q^{21} + 808q^{22} - 570q^{24} + 82q^{25} + 1484q^{28} + 677q^{30} - 1260q^{31} - 1449q^{33} + 344q^{36} - 222q^{37} - 649q^{39} - 2328q^{40} + 116q^{42} + 1280q^{43} + 2088q^{45} + 286q^{46} - 1028q^{49} + 472q^{51} - 786q^{52} + 39q^{54} + 2172q^{57} - 170q^{58} - 2947q^{60} - 18q^{61} - 455q^{63} + 27864q^{64} - 183q^{66} + 1002q^{67} + 4692q^{70} + 1089q^{72} - 1818q^{73} - 6102q^{75} - 4550q^{78} - 594q^{79} + 209q^{81} - 8628q^{82} + 1437q^{84} - 8548q^{85} + 3465q^{87} - 5298q^{88} + 5148q^{91} + 3812q^{93} + 270q^{94} - 4329q^{96} + 516q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database