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Properties

Label 525.4.bp
Level $525$
Weight $4$
Character orbit 525.bp
Rep. character $\chi_{525}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
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.bp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 15 q^{3} + 922 q^{4} - 3 q^{9} + O(q^{10}) \) \( 1888 q - 15 q^{3} + 922 q^{4} - 3 q^{9} - 60 q^{10} - 15 q^{12} + 306 q^{15} + 3610 q^{16} - 18 q^{19} + 99 q^{21} + 680 q^{22} - 246 q^{24} - 170 q^{25} - 300 q^{28} + 313 q^{30} + 1224 q^{31} + 2385 q^{33} - 880 q^{36} - 10 q^{37} - 541 q^{39} - 60 q^{40} - 2170 q^{42} + 2088 q^{45} - 298 q^{46} - 1028 q^{49} - 488 q^{51} - 30 q^{52} - 57 q^{54} - 3430 q^{58} - 1189 q^{60} - 18 q^{61} - 3175 q^{63} - 25192 q^{64} + 2757 q^{66} - 10 q^{67} + 4580 q^{70} - 645 q^{72} + 6810 q^{73} - 8130 q^{75} + 250 q^{78} - 594 q^{79} - 215 q^{81} + 3355 q^{84} + 7764 q^{85} - 15 q^{87} + 7010 q^{88} - 5172 q^{91} + 270 q^{94} + 1719 q^{96} + 516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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