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Properties

Label 3100.3.ee
Level $3100$
Weight $3$
Character orbit 3100.ee
Rep. character $\chi_{3100}(691,\cdot)$
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.ee (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

\( 7648 q - 2 q^{2} - 2 q^{4} - 8 q^{5} + 29 q^{6} - 20 q^{8} - 2860 q^{9} + O(q^{10}) \) \( 7648 q - 2 q^{2} - 2 q^{4} - 8 q^{5} + 29 q^{6} - 20 q^{8} - 2860 q^{9} - 14 q^{10} - 26 q^{12} - 16 q^{13} + 19 q^{14} - 2 q^{16} - 16 q^{17} + q^{18} - 87 q^{20} + 66 q^{21} + 89 q^{22} - 81 q^{24} + 16 q^{25} - 50 q^{26} - 94 q^{28} - 24 q^{29} - 139 q^{30} + 228 q^{32} + 164 q^{33} + 20 q^{34} - 40 q^{36} - 6 q^{37} - 91 q^{38} + 40 q^{40} - 16 q^{41} - 625 q^{42} - 175 q^{44} - 160 q^{45} + 46 q^{46} - 21 q^{48} - 6880 q^{49} - 108 q^{50} - 325 q^{52} - 592 q^{53} - 142 q^{54} - 11 q^{56} - 124 q^{57} + 202 q^{58} + 178 q^{60} - 24 q^{61} + 117 q^{62} + 268 q^{64} - 118 q^{65} + 1100 q^{66} - 471 q^{68} + 488 q^{69} - 119 q^{70} - 479 q^{72} - 352 q^{73} + 210 q^{74} - 430 q^{76} + 388 q^{77} + 73 q^{78} + 65 q^{80} + 8264 q^{81} - 220 q^{82} + 171 q^{84} - 16 q^{85} + 134 q^{86} + 113 q^{88} - 4 q^{89} + 543 q^{90} - 33 q^{92} + 802 q^{93} + 121 q^{94} + 34 q^{96} + 236 q^{97} + 1294 q^{98} + O(q^{100}) \)

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.