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Properties

Label 2475.4.gg
Level $2475$
Weight $4$
Character orbit 2475.gg
Rep. character $\chi_{2475}(13,\cdot)$
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.gg (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

\( 17216 q - 10 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{7} + 120 q^{8} - 180 q^{9} + O(q^{10}) \) \( 17216 q - 10 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{7} + 120 q^{8} - 180 q^{9} - 6 q^{11} - 36 q^{12} - 10 q^{13} - 20 q^{15} - 34050 q^{16} - 40 q^{17} - 20 q^{18} - 40 q^{19} - 6 q^{20} + 24 q^{22} + 216 q^{23} - 640 q^{24} + 138 q^{25} - 48 q^{26} + 580 q^{27} - 200 q^{28} - 10 q^{29} - 20 q^{30} - 2 q^{31} - 936 q^{33} - 20 q^{34} - 40 q^{35} - 792 q^{36} - 600 q^{37} + 74 q^{38} - 1420 q^{39} - 10 q^{40} - 10 q^{41} - 4220 q^{42} - 40 q^{44} + 1396 q^{45} + 770 q^{47} + 3976 q^{48} - 10 q^{50} - 40 q^{51} + 1270 q^{52} + 1536 q^{53} + 5520 q^{54} - 532 q^{55} - 268 q^{56} - 580 q^{57} + 1098 q^{58} + 5288 q^{60} - 10 q^{61} - 40 q^{62} + 3410 q^{63} + 1240 q^{64} - 1308 q^{66} + 596 q^{67} - 10 q^{68} - 20 q^{69} - 1506 q^{70} - 3728 q^{71} - 3390 q^{72} - 40 q^{73} + 4988 q^{75} - 796 q^{77} + 624 q^{78} + 2500 q^{79} - 1552 q^{80} - 964 q^{81} + 40 q^{82} - 4710 q^{83} - 4360 q^{84} - 10 q^{85} - 2 q^{86} + 6080 q^{87} + 2272 q^{88} + 13520 q^{89} + 8460 q^{90} - 8 q^{91} + 3230 q^{92} + 26108 q^{93} - 20 q^{94} + 1240 q^{95} + 620 q^{96} - 1158 q^{97} - 6860 q^{98} + O(q^{100}) \)

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.