Properties

Label 525.2.bh
Level 525
Weight 2
Character orbit bh
Rep. character \(\chi_{525}(13,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 320
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.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

Trace form

\( 320q + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 320q + 8q^{7} - 24q^{8} - 8q^{15} + 80q^{16} - 24q^{22} + 36q^{28} - 40q^{29} - 32q^{30} - 48q^{32} + 28q^{35} + 80q^{36} - 32q^{37} + 16q^{42} - 144q^{43} - 288q^{50} + 136q^{53} - 8q^{57} - 32q^{58} - 40q^{60} - 8q^{63} - 120q^{64} - 40q^{65} + 32q^{67} - 40q^{70} - 24q^{72} + 24q^{77} + 8q^{78} + 80q^{81} - 80q^{84} - 48q^{85} - 56q^{88} + 40q^{92} + 96q^{93} - 88q^{95} - 184q^{98} + O(q^{100}) \)

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.bh.a \(320\) \(4.192\) None \(0\) \(0\) \(0\) \(8\)

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