↑

Properties

Label 3100.3.ff
Level $3100$
Weight $3$
Character orbit 3100.ff
Rep. character $\chi_{3100}(479,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $7648$
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.ff (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3100 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 7712 7712 0
Cusp forms 7648 7648 0
Eisenstein series 64 64 0

Trace form

\( 7648 q - 10 q^{2} - 2 q^{4} - 8 q^{5} + 25 q^{6} - 10 q^{8} + 2828 q^{9} + O(q^{10}) \) \( 7648 q - 10 q^{2} - 2 q^{4} - 8 q^{5} + 25 q^{6} - 10 q^{8} + 2828 q^{9} - 4 q^{10} - 15 q^{12} - 20 q^{13} + 30 q^{14} - 2 q^{16} - 20 q^{17} - 40 q^{18} + q^{20} - 88 q^{21} - 240 q^{22} - 90 q^{24} + 8 q^{25} - 71 q^{26} - 10 q^{28} - 4 q^{29} - 88 q^{30} + 10 q^{33} - 16 q^{34} + 518 q^{36} - 10 q^{37} - 175 q^{38} - 73 q^{40} - 6 q^{41} - 15 q^{42} - 180 q^{44} - 76 q^{45} + 30 q^{46} - 10 q^{48} + 6568 q^{49} + 2 q^{50} - 145 q^{52} - 1110 q^{53} - 160 q^{54} + 250 q^{56} - 33 q^{60} - 24 q^{61} + 215 q^{62} - 182 q^{64} + 82 q^{65} - 166 q^{66} + 240 q^{68} - 300 q^{69} + 384 q^{70} - 1285 q^{72} - 20 q^{73} - 41 q^{74} + 410 q^{76} - 55 q^{78} + 884 q^{80} + 8426 q^{81} + 505 q^{82} + 37 q^{84} + 152 q^{85} + 600 q^{86} + 810 q^{88} - 4 q^{89} + 428 q^{90} - 710 q^{92} + 65 q^{94} - 110 q^{96} - 20 q^{97} - 25 q^{98} + O(q^{100}) \)

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.