Properties

Label 525.4.w
Level $525$
Weight $4$
Character orbit 525.w
Rep. character $\chi_{525}(104,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $944$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

Trace form

\( 944q - 940q^{4} - 6q^{9} + O(q^{10}) \) \( 944q - 940q^{4} - 6q^{9} + 198q^{15} - 3532q^{16} - 108q^{21} + 340q^{22} - 232q^{25} + 270q^{28} + 326q^{30} - 128q^{36} - 20q^{37} + 1114q^{39} - 1085q^{42} + 1540q^{46} + 980q^{49} - 1300q^{51} + 3400q^{58} + 2656q^{60} + 3160q^{63} - 11972q^{64} - 20q^{67} - 3020q^{70} + 630q^{72} - 280q^{78} - 1188q^{79} - 2482q^{81} - 2068q^{84} - 6948q^{85} + 8080q^{88} - 1020q^{91} - 4116q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database