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Properties

Label 3100.3.dd
Level $3100$
Weight $3$
Character orbit 3100.dd
Rep. character $\chi_{3100}(23,\cdot)$
Character field $\Q(\zeta_{20})$
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.dd (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3100 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 7648 q - 6 q^{2} - 10 q^{4} - 32 q^{5} - 12 q^{8} + O(q^{10}) \) \( 7648 q - 6 q^{2} - 10 q^{4} - 32 q^{5} - 12 q^{8} - 6 q^{10} + 80 q^{12} - 20 q^{13} + 140 q^{14} - 2 q^{16} - 20 q^{17} + 54 q^{18} - 50 q^{20} - 20 q^{21} - 50 q^{22} - 32 q^{25} - 158 q^{28} - 20 q^{29} - 100 q^{30} + 4 q^{32} + 24 q^{33} - 10 q^{34} + 20 q^{36} + 38 q^{38} + 174 q^{40} - 4 q^{41} - 10 q^{42} - 360 q^{44} + 288 q^{45} - 10 q^{48} - 400 q^{49} + 1178 q^{50} + 100 q^{52} + 700 q^{53} + 350 q^{54} - 12 q^{56} - 180 q^{57} - 10 q^{58} + 150 q^{60} - 62 q^{62} - 10 q^{64} - 20 q^{65} - 74 q^{66} + 660 q^{68} - 20 q^{69} + 188 q^{70} + 962 q^{72} - 20 q^{73} - 44 q^{76} - 20 q^{77} - 188 q^{78} + 1228 q^{80} - 66552 q^{81} - 200 q^{82} - 20 q^{84} - 20 q^{85} - 640 q^{88} - 40 q^{89} + 1554 q^{90} - 1170 q^{92} - 1708 q^{93} + 1030 q^{94} + 148 q^{97} - 938 q^{98} + O(q^{100}) \)

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.