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Properties

Label 2475.4.fd
Level $2475$
Weight $4$
Character orbit 2475.fd
Rep. character $\chi_{2475}(281,\cdot)$
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.fd (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

\( 8608 q - 15 q^{2} - 16 q^{3} + 4287 q^{4} + 3 q^{5} - 50 q^{6} - 10 q^{7} - 44 q^{9} + O(q^{10}) \) \( 8608 q - 15 q^{2} - 16 q^{3} + 4287 q^{4} + 3 q^{5} - 50 q^{6} - 10 q^{7} - 44 q^{9} - 80 q^{10} - 9 q^{11} + 254 q^{12} - 3 q^{14} - 355 q^{15} + 17055 q^{16} - 20 q^{18} - 20 q^{19} - 249 q^{20} + 135 q^{21} - 35 q^{22} - 18 q^{23} + 340 q^{24} - 75 q^{25} - 604 q^{27} - 20 q^{28} - 15 q^{29} - 280 q^{30} - 55 q^{31} - 363 q^{33} - 14 q^{34} + 1054 q^{36} + 140 q^{37} - 135 q^{38} - 5 q^{40} - 15 q^{41} + 196 q^{42} - 873 q^{45} - 20 q^{46} + 9294 q^{47} + 2745 q^{48} - 51554 q^{49} - 15 q^{50} + 250 q^{51} - 645 q^{52} + 2680 q^{54} - 3464 q^{55} - 1023 q^{56} + 540 q^{57} - 1073 q^{58} + 1491 q^{59} - 4004 q^{60} + 1705 q^{63} - 134644 q^{64} - 7110 q^{65} + 3846 q^{66} + 912 q^{67} + 930 q^{68} + 221 q^{69} + 364 q^{70} + 5110 q^{72} - 20 q^{73} + 90 q^{74} - 1086 q^{75} + 39 q^{77} + 3326 q^{78} - 635 q^{79} - 1484 q^{81} - 8 q^{82} + 7035 q^{83} + 2245 q^{84} - 5 q^{85} - 3 q^{86} - 270 q^{87} - 1307 q^{88} + 9610 q^{90} - 690 q^{91} + 18810 q^{92} + 6775 q^{93} - 85 q^{94} - 15 q^{95} + 1151 q^{97} - 467 q^{99} + O(q^{100}) \)

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.