Properties

Label 2475.4.gj
Level $2475$
Weight $4$
Character orbit 2475.gj
Rep. character $\chi_{2475}(502,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $17216$
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.gj (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 17344 17344 0
Cusp forms 17216 17216 0
Eisenstein series 128 128 0

Trace form

\( 17216 q - 10 q^{2} - 28 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 200 q^{8} + 140 q^{9} + O(q^{10}) \) \( 17216 q - 10 q^{2} - 28 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 200 q^{8} + 140 q^{9} - 6 q^{11} - 226 q^{12} - 10 q^{13} - 10 q^{14} - 20 q^{15} + 136180 q^{16} - 40 q^{17} - 20 q^{18} - 80 q^{19} - 646 q^{20} - 136 q^{22} + 216 q^{23} - 640 q^{24} + 138 q^{25} - 48 q^{26} - 2380 q^{27} + 120 q^{28} - 20 q^{29} - 20 q^{30} - 2 q^{31} + 800 q^{32} - 186 q^{33} - 20 q^{34} - 40 q^{35} - 132 q^{36} + 120 q^{37} - 6 q^{38} - 20 q^{39} + 630 q^{40} - 10 q^{41} + 4640 q^{42} - 1320 q^{44} + 146 q^{45} - 40 q^{46} + 770 q^{47} - 2794 q^{48} - 1130 q^{50} - 40 q^{51} - 1290 q^{52} + 4936 q^{53} + 5520 q^{54} - 532 q^{55} - 268 q^{56} - 580 q^{57} + 1098 q^{58} - 10 q^{59} - 312 q^{60} - 10 q^{61} - 40 q^{62} - 20 q^{63} + 852 q^{66} + 596 q^{67} + 630 q^{68} + 994 q^{70} + 2472 q^{71} - 100 q^{72} - 40 q^{73} + 4988 q^{75} - 796 q^{77} - 4216 q^{78} - 1270 q^{79} + 2848 q^{80} - 964 q^{81} + 40 q^{82} - 10 q^{83} + 2140 q^{84} - 10 q^{85} - 12 q^{86} + 270 q^{87} - 4128 q^{88} - 80 q^{89} - 20 q^{90} - 8 q^{91} - 13980 q^{92} - 4002 q^{93} - 8290 q^{94} - 1260 q^{95} - 660 q^{96} - 1158 q^{97} + 1370 q^{99} + O(q^{100}) \)

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

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