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Properties

Label 3100.3.gd
Level $3100$
Weight $3$
Character orbit 3100.gd
Rep. character $\chi_{3100}(127,\cdot)$
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.gd (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

\( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} - 24 q^{8} - 40 q^{9} + O(q^{10}) \) \( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} - 24 q^{8} - 40 q^{9} - 18 q^{10} + 40 q^{12} - 28 q^{13} - 20 q^{14} - 4 q^{16} - 28 q^{17} + 18 q^{18} - 20 q^{20} - 16 q^{21} - 248 q^{22} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 40 q^{29} - 2 q^{32} + 180 q^{33} - 20 q^{34} - 230 q^{36} - 48 q^{37} - 160 q^{38} + 72 q^{40} - 12 q^{41} - 860 q^{42} - 20 q^{44} + 164 q^{45} - 20 q^{46} - 68 q^{48} - 326 q^{50} - 218 q^{52} - 1036 q^{53} - 40 q^{54} - 6 q^{56} - 48 q^{57} - 20 q^{58} - 320 q^{60} - 396 q^{62} - 20 q^{64} - 28 q^{65} + 68 q^{66} - 26 q^{68} - 60 q^{69} - 944 q^{70} - 60 q^{72} - 28 q^{73} - 550 q^{74} - 292 q^{76} - 40 q^{77} + 218 q^{78} + 644 q^{80} - 16664 q^{81} - 890 q^{82} - 20 q^{84} - 40 q^{85} - 8 q^{86} - 1398 q^{88} - 40 q^{89} - 372 q^{90} - 1380 q^{92} - 20 q^{93} + 1010 q^{94} - 188 q^{96} - 184 q^{97} - 84 q^{98} + O(q^{100}) \)

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.