Properties

Label 525.2.w
Level 525
Weight 2
Character orbit w
Rep. character \(\chi_{525}(104,\cdot)\)
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.w (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

\( 304q - 84q^{4} - 6q^{9} + O(q^{10}) \) \( 304q - 84q^{4} - 6q^{9} - 36q^{15} - 60q^{16} - 18q^{21} - 40q^{22} - 8q^{25} + 60q^{28} + 14q^{30} + 28q^{36} - 20q^{37} - 2q^{39} - 35q^{42} - 24q^{46} - 20q^{49} - 52q^{51} - 80q^{58} + 4q^{60} + 55q^{63} - 76q^{64} - 20q^{67} + 6q^{70} + 30q^{72} - 40q^{78} - 68q^{79} - 10q^{81} + 80q^{84} - 88q^{85} - 20q^{88} - 82q^{91} - 36q^{99} + O(q^{100}) \)

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.w.a \(304\) \(4.192\) None \(0\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database