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Properties

Label 525.4.bo
Level $525$
Weight $4$
Character orbit 525.bo
Rep. character $\chi_{525}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $960$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960 q - 480 q^{4} + 8 q^{5} - 48 q^{6} - 420 q^{8} - 1080 q^{9} + O(q^{10}) \) \( 960 q - 480 q^{4} + 8 q^{5} - 48 q^{6} - 420 q^{8} - 1080 q^{9} - 18 q^{10} - 84 q^{11} + 132 q^{14} + 84 q^{15} + 1920 q^{16} - 640 q^{17} - 304 q^{19} + 952 q^{20} - 720 q^{22} + 720 q^{23} + 1152 q^{24} - 210 q^{25} + 360 q^{28} - 96 q^{29} + 576 q^{30} + 330 q^{31} + 800 q^{34} + 204 q^{35} - 8640 q^{36} + 2490 q^{38} + 438 q^{40} - 576 q^{41} + 1020 q^{42} - 896 q^{44} - 72 q^{45} + 228 q^{46} + 516 q^{49} + 3932 q^{50} - 4170 q^{52} + 4320 q^{53} - 216 q^{54} - 2084 q^{55} + 2700 q^{56} - 3420 q^{58} + 984 q^{59} - 1614 q^{60} + 2120 q^{61} - 6960 q^{62} + 180 q^{63} + 11436 q^{64} - 660 q^{65} + 1056 q^{66} - 4620 q^{67} + 2208 q^{69} + 7410 q^{70} - 1472 q^{71} + 1890 q^{72} + 2280 q^{73} + 2988 q^{74} + 312 q^{75} + 25544 q^{76} + 1084 q^{79} + 5944 q^{80} + 9720 q^{81} - 13840 q^{83} + 6768 q^{84} - 12088 q^{85} + 336 q^{86} - 6250 q^{88} + 216 q^{90} + 1884 q^{91} + 13860 q^{92} - 3104 q^{94} + 4448 q^{95} - 1182 q^{96} + 13020 q^{97} - 33720 q^{98} + 1008 q^{99} + O(q^{100}) \)

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.

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)