Properties

Label 525.2.bm
Level 525
Weight 2
Character orbit bm
Rep. character \(\chi_{525}(131,\cdot)\)
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.bm (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

\( 608q - 9q^{3} - 78q^{4} - 36q^{7} - 3q^{9} + O(q^{10}) \) \( 608q - 9q^{3} - 78q^{4} - 36q^{7} - 3q^{9} - 30q^{10} + 3q^{12} + 16q^{15} + 50q^{16} - 8q^{18} - 18q^{19} - 21q^{21} - 24q^{22} - 66q^{24} - 10q^{25} - 30q^{28} - 7q^{30} - 36q^{31} + 36q^{33} - 100q^{36} - 14q^{37} - 31q^{39} - 30q^{40} + 20q^{42} - 96q^{43} - 117q^{45} + 42q^{46} - 28q^{49} - 8q^{51} - 66q^{52} + 3q^{54} + 48q^{57} - 38q^{58} - 49q^{60} - 18q^{61} + 4q^{63} - 32q^{64} - 3q^{66} - 22q^{67} - 270q^{70} + 45q^{72} + 102q^{73} + 135q^{75} + 58q^{78} - 34q^{79} - 55q^{81} + 108q^{82} - 75q^{84} - 96q^{85} - 9q^{87} + 36q^{88} + 38q^{91} - 22q^{93} + 30q^{94} - 81q^{96} + 36q^{99} + O(q^{100}) \)

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.bm.a \(608\) \(4.192\) None \(0\) \(-9\) \(0\) \(-36\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database