Properties

Label 525.2.bo
Level 525
Weight 2
Character orbit bo
Rep. character \(\chi_{525}(4,\cdot)\)
Character field \(\Q(\zeta_{30})\)
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

Trace form

\( 320q - 40q^{4} - 2q^{5} + 8q^{6} + 60q^{8} - 40q^{9} + O(q^{10}) \) \( 320q - 40q^{4} - 2q^{5} + 8q^{6} + 60q^{8} - 40q^{9} + 4q^{10} - 6q^{11} + 12q^{14} + 4q^{15} + 40q^{16} - 20q^{17} + 16q^{19} + 8q^{20} + 40q^{22} - 60q^{23} - 48q^{24} + 4q^{25} - 30q^{28} + 24q^{29} - 48q^{30} - 30q^{31} - 80q^{36} + 30q^{38} - 32q^{40} + 36q^{41} + 10q^{42} - 16q^{44} + 2q^{45} + 32q^{46} + 16q^{49} - 140q^{50} + 190q^{52} - 60q^{53} + 4q^{54} - 8q^{55} + 60q^{58} + 24q^{59} - 46q^{60} - 20q^{61} + 120q^{62} + 10q^{63} - 4q^{64} - 30q^{65} - 16q^{66} - 60q^{67} - 32q^{69} - 76q^{70} + 32q^{71} - 30q^{72} - 40q^{73} - 12q^{74} - 8q^{75} - 344q^{76} + 4q^{79} - 52q^{80} + 40q^{81} - 80q^{83} + 48q^{84} - 76q^{85} + 24q^{86} - 200q^{88} - 52q^{90} + 26q^{91} + 180q^{92} + 16q^{94} - 38q^{95} - 58q^{96} - 140q^{97} + 360q^{98} + 8q^{99} + O(q^{100}) \)

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.bo.a \(320\) \(4.192\) None \(0\) \(0\) \(-2\) \(0\)

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