Properties

Label 525.4.bb
Level $525$
Weight $4$
Character orbit 525.bb
Rep. character $\chi_{525}(41,\cdot)$
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.bb (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

\( 944q + 916q^{4} - 28q^{7} - 6q^{9} + O(q^{10}) \) \( 944q + 916q^{4} - 28q^{7} - 6q^{9} - 46q^{15} - 3660q^{16} - 64q^{18} + 102q^{21} - 196q^{22} + 272q^{25} - 206q^{28} - 86q^{30} + 628q^{36} + 204q^{37} + 898q^{39} + 1027q^{42} - 1376q^{43} - 1564q^{46} + 980q^{49} + 1268q^{51} + 1596q^{57} - 6496q^{58} + 544q^{60} - 2158q^{63} + 14844q^{64} + 2004q^{67} + 3636q^{70} - 4218q^{72} + 6212q^{78} - 1188q^{79} + 2470q^{81} - 150q^{84} + 3532q^{85} - 9168q^{88} + 1008q^{91} + 2884q^{93} - 4116q^{99} + O(q^{100}) \)

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