Properties

Label 525.2.bs
Level 525
Weight 2
Character orbit bs
Rep. character \(\chi_{525}(2,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1216
Newform subspaces 1
Sturm bound 160
Trace bound 0

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 1344 1344 0
Cusp forms 1216 1216 0
Eisenstein series 128 128 0

Trace form

\( 1216q - 8q^{3} - 20q^{4} - 24q^{6} - 28q^{7} - 10q^{9} + O(q^{10}) \) \( 1216q - 8q^{3} - 20q^{4} - 24q^{6} - 28q^{7} - 10q^{9} - 12q^{10} - 64q^{13} - 44q^{15} - 140q^{16} - 24q^{18} - 20q^{19} - 12q^{21} + 8q^{22} - 24q^{25} - 80q^{27} - 40q^{28} - 50q^{30} - 12q^{31} - 6q^{33} - 80q^{34} + 8q^{36} - 24q^{37} - 50q^{39} - 4q^{40} - 34q^{42} - 96q^{43} + 30q^{45} - 12q^{46} - 44q^{48} - 16q^{51} - 136q^{52} - 10q^{54} - 40q^{55} - 112q^{57} - 76q^{58} - 60q^{60} - 12q^{61} - 14q^{63} - 80q^{64} - 30q^{66} - 32q^{67} + 100q^{69} - 100q^{70} + 24q^{72} - 72q^{73} - 96q^{75} - 64q^{76} + 20q^{78} - 20q^{79} - 6q^{81} - 204q^{82} + 100q^{84} - 56q^{85} + 36q^{87} - 140q^{88} + 164q^{90} - 24q^{91} + 34q^{93} - 20q^{94} - 30q^{96} - 240q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.2.bs.a \(1216\) \(4.192\) None \(0\) \(-8\) \(0\) \(-28\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database