↑

Properties

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

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3100.gh (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

\( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} + 36 q^{8} - 40 q^{9} + O(q^{10}) \) \( 15296 q - 12 q^{2} - 20 q^{4} - 16 q^{5} - 18 q^{6} + 36 q^{8} - 40 q^{9} - 18 q^{10} + 40 q^{12} - 28 q^{13} - 30 q^{14} - 4 q^{16} - 28 q^{17} + 28 q^{18} - 70 q^{20} - 36 q^{21} + 52 q^{22} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 80 q^{29} - 100 q^{30} - 52 q^{32} - 20 q^{34} + 250 q^{36} - 48 q^{37} - 90 q^{38} + 72 q^{40} - 32 q^{41} - 440 q^{42} - 10 q^{44} + 164 q^{45} - 20 q^{46} - 68 q^{48} + 800 q^{49} - 326 q^{50} - 218 q^{52} + 404 q^{53} - 20 q^{54} - 6 q^{56} - 228 q^{57} - 20 q^{58} - 20 q^{60} + 54 q^{62} + 880 q^{64} - 28 q^{65} - 312 q^{66} + 804 q^{68} - 1240 q^{69} + 726 q^{70} - 510 q^{72} - 588 q^{73} + 188 q^{76} - 40 q^{77} - 222 q^{78} - 706 q^{80} - 16664 q^{81} + 200 q^{82} - 20 q^{84} - 40 q^{85} - 8 q^{86} + 872 q^{88} - 40 q^{89} - 282 q^{90} - 1170 q^{92} + 160 q^{93} - 1090 q^{94} - 188 q^{96} - 184 q^{97} + 1616 q^{98} + O(q^{100}) \)

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.