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Properties

Label 525.4.bk
Level $525$
Weight $4$
Character orbit 525.bk
Rep. character $\chi_{525}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1952 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

Trace form

\( 1440 q - 8 q^{3} + O(q^{10}) \) \( 1440 q - 8 q^{3} - 144 q^{10} + 128 q^{12} + 144 q^{13} + 16 q^{15} + 5760 q^{16} - 460 q^{18} - 240 q^{19} + 144 q^{22} + 2376 q^{25} + 592 q^{27} + 580 q^{30} + 56 q^{33} - 5280 q^{34} - 2088 q^{37} - 2440 q^{39} - 144 q^{40} - 560 q^{42} - 240 q^{43} + 880 q^{45} + 9012 q^{48} - 240 q^{52} + 7540 q^{54} - 1200 q^{55} + 1112 q^{57} - 840 q^{58} + 6308 q^{60} - 4256 q^{63} + 5760 q^{64} + 1392 q^{67} + 1008 q^{70} - 18744 q^{72} - 7536 q^{73} - 5280 q^{75} - 7900 q^{78} - 4320 q^{79} + 1280 q^{81} - 18240 q^{82} - 13224 q^{85} + 8592 q^{87} + 18672 q^{88} + 5664 q^{90} + 10848 q^{93} + 38640 q^{94} + 7872 q^{97} + O(q^{100}) \)

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.

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)