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Properties

Label 2475.4.gk
Level $2475$
Weight $4$
Character orbit 2475.gk
Rep. character $\chi_{2475}(113,\cdot)$
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.gk (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

\( 17216 q - 18 q^{2} + 4 q^{3} - 18 q^{5} - 4 q^{6} - 6 q^{7} + 140 q^{9} + O(q^{10}) \) \( 17216 q - 18 q^{2} + 4 q^{3} - 18 q^{5} - 4 q^{6} - 6 q^{7} + 140 q^{9} - 64 q^{10} - 18 q^{11} - 98 q^{12} - 6 q^{13} - 30 q^{14} - 4 q^{15} + 136180 q^{16} - 44 q^{18} - 402 q^{20} - 24 q^{21} - 136 q^{22} - 48 q^{23} - 640 q^{24} + 138 q^{25} + 2356 q^{27} - 1976 q^{28} + 488 q^{30} - 2 q^{31} - 1200 q^{32} - 78 q^{33} - 20 q^{34} - 132 q^{36} - 168 q^{37} - 18 q^{38} - 20 q^{39} + 378 q^{40} - 6 q^{41} + 2696 q^{42} - 16 q^{43} - 210 q^{45} - 8 q^{46} - 2346 q^{47} + 7446 q^{48} + 1998 q^{50} - 24 q^{51} - 806 q^{52} + 5480 q^{54} + 468 q^{55} - 36 q^{56} + 516 q^{57} - 918 q^{58} - 30 q^{59} + 3144 q^{60} - 2 q^{61} + 200 q^{63} - 48 q^{65} + 852 q^{66} - 628 q^{67} - 1170 q^{68} - 1006 q^{70} + 1632 q^{72} - 24 q^{73} - 5012 q^{75} + 736 q^{76} + 6456 q^{77} + 4248 q^{78} - 1270 q^{79} - 964 q^{81} + 40 q^{82} - 5658 q^{83} - 2180 q^{84} - 6 q^{85} - 36 q^{86} + 2562 q^{87} + 48 q^{88} - 20904 q^{90} - 8 q^{91} + 28464 q^{92} + 3822 q^{93} - 8290 q^{94} + 2232 q^{95} + 2460 q^{96} - 1158 q^{97} - 1370 q^{99} + O(q^{100}) \)

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.