Properties

Label 525.2.bv
Level 525
Weight 2
Character orbit bv
Rep. character \(\chi_{525}(52,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 640
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 640 704
Cusp forms 1216 640 576
Eisenstein series 128 0 128

Trace form

\( 640q + 12q^{5} - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 640q + 12q^{5} - 8q^{7} + 24q^{8} + 12q^{10} + 8q^{15} - 80q^{16} - 72q^{22} + 48q^{23} - 12q^{25} - 36q^{28} - 80q^{29} + 32q^{30} - 24q^{32} + 36q^{33} - 64q^{35} + 160q^{36} - 4q^{37} - 192q^{38} - 12q^{40} - 16q^{42} + 120q^{43} + 60q^{47} + 288q^{50} - 432q^{52} - 136q^{53} - 16q^{57} - 4q^{58} - 240q^{59} - 20q^{60} - 4q^{63} + 120q^{64} + 4q^{65} - 8q^{67} - 132q^{68} + 76q^{70} - 12q^{72} - 36q^{73} - 48q^{75} - 60q^{77} - 80q^{78} + 12q^{80} - 80q^{81} - 252q^{82} - 160q^{84} + 72q^{85} + 24q^{87} + 152q^{88} + 56q^{92} - 96q^{93} + 172q^{95} - 488q^{98} + O(q^{100}) \)

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.bv.a \(640\) \(4.192\) None \(0\) \(0\) \(12\) \(-8\)

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database