Properties

Label 525.2.bb
Level 525
Weight 2
Character orbit bb
Rep. character \(\chi_{525}(41,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 304
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.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 525 \)
Character field: \(\Q(\zeta_{10})\)
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 336 336 0
Cusp forms 304 304 0
Eisenstein series 32 32 0

Trace form

\( 304q + 60q^{4} - 12q^{7} - 6q^{9} + O(q^{10}) \) \( 304q + 60q^{4} - 12q^{7} - 6q^{9} + 8q^{15} - 92q^{16} - 16q^{18} + 12q^{21} - 48q^{22} - 32q^{25} - 36q^{28} - 14q^{30} - 8q^{36} - 4q^{37} - 26q^{39} - 11q^{42} - 20q^{49} + 20q^{51} - 168q^{57} + 32q^{58} + 76q^{60} + 29q^{63} + 68q^{64} - 44q^{67} + 30q^{70} - 114q^{72} - 124q^{78} - 68q^{79} - 2q^{81} + 102q^{84} + 72q^{85} - 156q^{88} + 70q^{91} - 32q^{93} - 36q^{99} + O(q^{100}) \)

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.bb.a \(304\) \(4.192\) None \(0\) \(0\) \(0\) \(-12\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database