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Properties

Label 3100.3.fl
Level $3100$
Weight $3$
Character orbit 3100.fl
Rep. character $\chi_{3100}(431,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $7648$
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.fl (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

\( 7648 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 31 q^{6} + 10 q^{8} + 11370 q^{9} + O(q^{10}) \) \( 7648 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 31 q^{6} + 10 q^{8} + 11370 q^{9} - 14 q^{10} - 116 q^{12} - 16 q^{13} - 81 q^{14} - 2 q^{16} - 16 q^{17} + q^{18} + 18 q^{20} - 34 q^{21} + 49 q^{22} - 81 q^{24} + 16 q^{25} - 50 q^{26} + 181 q^{28} - 4 q^{29} - 139 q^{30} + 228 q^{32} - 276 q^{33} - 40 q^{34} + 200 q^{36} - 6 q^{37} + 64 q^{38} + 40 q^{40} - 16 q^{41} + 95 q^{42} + 75 q^{44} + 180 q^{45} - 44 q^{46} + 19 q^{48} - 6880 q^{49} + 147 q^{50} - 85 q^{52} + 488 q^{53} + 28 q^{54} - 11 q^{56} - 124 q^{57} - 348 q^{58} + 293 q^{60} - 24 q^{61} - 68 q^{62} - 182 q^{64} - 118 q^{65} + 10 q^{66} - 471 q^{68} - 382 q^{69} - 189 q^{70} + 201 q^{72} + 218 q^{73} + 210 q^{74} - 430 q^{76} - 592 q^{77} - 242 q^{78} + 855 q^{80} - 33216 q^{81} - 220 q^{82} + 81 q^{84} - 176 q^{85} - 611 q^{86} - 847 q^{88} - 24 q^{89} + 523 q^{90} - 33 q^{92} + 802 q^{93} + 121 q^{94} + 144 q^{96} - 164 q^{97} - 2336 q^{98} + O(q^{100}) \)

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.