Properties

Label 525.4.b
Level $525$
Weight $4$
Character orbit 525.b
Rep. character $\chi_{525}(251,\cdot)$
Character field $\Q$
Dimension $146$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 252 158 94
Cusp forms 228 146 82
Eisenstein series 24 12 12

Trace form

\( 146q - 556q^{4} - 42q^{9} + O(q^{10}) \) \( 146q - 556q^{4} - 42q^{9} + 1884q^{16} + 160q^{18} + 78q^{21} + 8q^{22} + 392q^{28} - 624q^{36} + 924q^{37} + 132q^{39} + 1380q^{42} - 120q^{43} + 40q^{46} + 766q^{49} - 624q^{51} + 936q^{57} - 2104q^{58} - 676q^{63} - 5124q^{64} + 8q^{67} - 3772q^{72} + 1800q^{78} + 1040q^{79} + 1002q^{81} - 3120q^{84} + 2368q^{88} - 68q^{91} + 2532q^{93} - 1128q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database