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Properties

Label 2475.4.ey
Level $2475$
Weight $4$
Character orbit 2475.ey
Rep. character $\chi_{2475}(761,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8608$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.ey (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - 15 q^{2} - 6 q^{3} + 4287 q^{4} + 3 q^{5} - 10 q^{6} - 10 q^{7} - 34 q^{9} + O(q^{10}) \) \( 8608 q - 15 q^{2} - 6 q^{3} + 4287 q^{4} + 3 q^{5} - 10 q^{6} - 10 q^{7} - 34 q^{9} - 9 q^{11} - 16 q^{12} - 5 q^{13} - 3 q^{14} - 35 q^{15} + 17015 q^{16} - 20 q^{18} - 20 q^{19} - 249 q^{20} - 35 q^{22} - 18 q^{23} - 340 q^{24} - 75 q^{25} - 594 q^{27} - 15 q^{29} + 730 q^{30} + 30 q^{31} - 228 q^{33} - 14 q^{34} - 1786 q^{36} + 140 q^{37} + 165 q^{38} - 575 q^{39} - 5 q^{40} + 4576 q^{42} - 348 q^{45} - 20 q^{46} - 2331 q^{47} + 2870 q^{48} - 51554 q^{49} + 1665 q^{50} - 290 q^{51} + 35 q^{52} - 2760 q^{54} + 846 q^{55} + 4122 q^{56} + 540 q^{57} + 1527 q^{58} - 999 q^{59} - 3869 q^{60} - 5 q^{61} - 134004 q^{64} + 2536 q^{66} + 912 q^{67} - 990 q^{68} + 356 q^{69} + 1614 q^{70} - 150 q^{74} - 4976 q^{75} + 39 q^{77} - 3664 q^{78} - 5 q^{79} + 766 q^{81} - 8 q^{82} - 15 q^{83} + 2245 q^{84} - 5 q^{85} - 3 q^{86} + 6080 q^{87} - 1347 q^{88} - 16920 q^{90} + 2720 q^{91} - 28485 q^{92} - 8415 q^{93} + 4135 q^{94} - 15 q^{95} + 1670 q^{96} - 1729 q^{97} + 218 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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