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Properties

Label 3100.3.gi
Level $3100$
Weight $3$
Character orbit 3100.gi
Rep. character $\chi_{3100}(327,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $15296$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3100.gi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3100 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3100, [\chi])\).

Total New Old
Modular forms 15424 15424 0
Cusp forms 15296 15296 0
Eisenstein series 128 128 0

Trace form

\( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} - 24 q^{8} - 60 q^{9} + O(q^{10}) \) \( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} - 24 q^{8} - 60 q^{9} - 18 q^{10} - 50 q^{12} - 28 q^{13} - 170 q^{14} - 4 q^{16} - 28 q^{17} - 102 q^{18} - 70 q^{20} - 16 q^{21} + 92 q^{22} - 16 q^{25} - 48 q^{26} + 230 q^{28} - 40 q^{29} + 100 q^{30} - 52 q^{32} - 60 q^{33} - 20 q^{34} - 230 q^{36} - 48 q^{37} + 10 q^{38} + 72 q^{40} - 32 q^{41} - 410 q^{42} + 810 q^{44} - 336 q^{45} - 68 q^{48} - 800 q^{49} + 574 q^{50} - 58 q^{52} - 316 q^{53} - 380 q^{54} - 6 q^{56} + 132 q^{57} - 20 q^{58} + 300 q^{60} + 134 q^{62} - 20 q^{64} - 28 q^{65} + 68 q^{66} - 846 q^{68} - 40 q^{69} + 676 q^{70} - 1970 q^{72} - 28 q^{73} + 188 q^{76} - 40 q^{77} + 218 q^{78} + 1274 q^{80} + 66516 q^{81} + 200 q^{82} - 10 q^{84} - 40 q^{85} - 18 q^{86} + 232 q^{88} - 80 q^{89} - 372 q^{90} + 1170 q^{92} + 1660 q^{93} - 1090 q^{94} + 702 q^{96} - 184 q^{97} - 2014 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3100, [\chi])\) into newform subspaces

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