↑

Properties

Label 2475.4.ge
Level $2475$
Weight $4$
Character orbit 2475.ge
Rep. character $\chi_{2475}(488,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $17216$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.ge (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

\( 17216 q - 18 q^{2} - 16 q^{3} - 10 q^{4} - 18 q^{5} - 4 q^{6} - 6 q^{7} + O(q^{10}) \) \( 17216 q - 18 q^{2} - 16 q^{3} - 10 q^{4} - 18 q^{5} - 4 q^{6} - 6 q^{7} - 64 q^{10} - 18 q^{11} - 98 q^{12} - 6 q^{13} - 30 q^{14} - 4 q^{15} - 34050 q^{16} + 116 q^{18} - 40 q^{19} - 402 q^{20} - 24 q^{21} + 24 q^{22} - 48 q^{23} + 640 q^{24} + 138 q^{25} - 604 q^{27} + 424 q^{28} - 30 q^{29} + 488 q^{30} - 2 q^{31} - 1200 q^{32} - 78 q^{33} - 20 q^{34} - 132 q^{36} - 168 q^{37} + 102 q^{38} - 262 q^{40} - 6 q^{41} - 1224 q^{42} - 16 q^{43} - 210 q^{45} - 8 q^{46} + 9294 q^{47} - 2904 q^{48} - 1362 q^{50} - 24 q^{51} + 474 q^{52} + 5480 q^{54} - 2032 q^{55} - 36 q^{56} - 564 q^{57} - 1078 q^{58} - 5010 q^{59} - 4426 q^{60} - 12 q^{61} - 3230 q^{63} - 40 q^{64} - 48 q^{65} - 1308 q^{66} - 628 q^{67} + 750 q^{68} - 3120 q^{69} + 1494 q^{70} - 7248 q^{72} - 24 q^{73} - 5012 q^{75} + 736 q^{76} + 6456 q^{77} + 4248 q^{78} + 1250 q^{79} + 616 q^{81} - 120 q^{82} + 8442 q^{83} + 2140 q^{84} - 6 q^{85} - 6 q^{86} + 2562 q^{87} + 1328 q^{88} + 18196 q^{90} - 8 q^{91} - 18846 q^{92} - 3808 q^{93} - 10 q^{94} - 1518 q^{95} - 1240 q^{96} - 1158 q^{97} + 1370 q^{99} + O(q^{100}) \)

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.