Properties

Label 525.2.bk
Level 525
Weight 2
Character orbit bk
Rep. character \(\chi_{525}(8,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 480
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.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
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 672 480 192
Cusp forms 608 480 128
Eisenstein series 64 0 64

Trace form

\( 480q + 4q^{3} + O(q^{10}) \) \( 480q + 4q^{3} + 16q^{10} - 16q^{12} + 8q^{13} + 16q^{15} + 120q^{16} + 20q^{18} - 40q^{19} - 48q^{22} - 104q^{25} + 16q^{27} - 20q^{30} - 28q^{33} - 80q^{34} + 16q^{37} - 40q^{39} - 64q^{40} - 80q^{42} + 40q^{43} - 20q^{45} - 276q^{48} - 260q^{54} - 40q^{55} - 4q^{57} - 40q^{58} - 52q^{60} - 32q^{63} + 160q^{64} + 56q^{67} + 8q^{70} + 288q^{72} + 48q^{73} + 60q^{75} + 140q^{78} + 80q^{79} - 40q^{81} - 184q^{85} + 96q^{87} - 56q^{88} + 24q^{90} + 96q^{93} - 560q^{94} - 24q^{97} + O(q^{100}) \)

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.bk.a \(480\) \(4.192\) None \(0\) \(4\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database