Properties

Label 525.2.bp
Level 525
Weight 2
Character orbit bp
Rep. character \(\chi_{525}(59,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 608
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.bp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{30})\)
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 672 672 0
Cusp forms 608 608 0
Eisenstein series 64 64 0

Trace form

\( 608q - 15q^{3} + 66q^{4} - 3q^{9} + O(q^{10}) \) \( 608q - 15q^{3} + 66q^{4} - 3q^{9} - 30q^{10} - 15q^{12} - 36q^{15} + 66q^{16} - 18q^{19} + 9q^{21} - 80q^{22} - 30q^{24} + 2q^{25} - 90q^{28} - 23q^{30} - 90q^{33} + 44q^{36} - 10q^{37} - 19q^{39} + 42q^{40} - 70q^{42} - 117q^{45} - 54q^{46} - 28q^{49} - 8q^{51} - 30q^{52} - 21q^{54} + 50q^{58} - 67q^{60} - 18q^{61} - 70q^{63} - 176q^{64} + 57q^{66} - 10q^{67} + 42q^{70} - 45q^{72} - 150q^{73} + 33q^{75} + 10q^{78} - 34q^{79} + 49q^{81} - 53q^{84} - 8q^{85} - 15q^{87} + 80q^{88} - 62q^{91} + 30q^{94} - 9q^{96} + 36q^{99} + O(q^{100}) \)

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.bp.a \(608\) \(4.192\) None \(0\) \(-15\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database