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Properties

Label 3100.3.bj
Level $3100$
Weight $3$
Character orbit 3100.bj
Rep. character $\chi_{3100}(219,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $3824$
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.bj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 3856 3856 0
Cusp forms 3824 3824 0
Eisenstein series 32 32 0

Trace form

\( 3824 q - 5 q^{2} - q^{4} - 16 q^{5} - 10 q^{6} - 20 q^{8} - 2846 q^{9} + O(q^{10}) \) \( 3824 q - 5 q^{2} - q^{4} - 16 q^{5} - 10 q^{6} - 20 q^{8} - 2846 q^{9} - 20 q^{10} - 5 q^{12} - 10 q^{13} - 20 q^{14} - q^{16} - 10 q^{17} + 65 q^{18} - 45 q^{20} + 60 q^{21} + 70 q^{22} - 15 q^{24} + 8 q^{25} + 68 q^{26} - 5 q^{28} - 12 q^{29} + 53 q^{30} - 10 q^{33} + 3 q^{34} - 231 q^{36} - 20 q^{37} + 79 q^{40} - 2 q^{41} + 170 q^{42} + 70 q^{44} + 178 q^{45} - 25 q^{46} - 6576 q^{49} - 158 q^{50} + 210 q^{52} + 350 q^{53} + 195 q^{54} + 10 q^{56} - 45 q^{58} - 257 q^{60} - 12 q^{61} + 220 q^{62} + 134 q^{64} - 106 q^{65} - 580 q^{66} + 700 q^{69} - 140 q^{70} - 10 q^{73} - 242 q^{74} + 160 q^{76} - 10 q^{77} - 140 q^{78} + 495 q^{80} - 8246 q^{81} - 110 q^{84} - 154 q^{85} + 165 q^{86} + 310 q^{88} - 2 q^{89} + 567 q^{90} - 250 q^{92} + 930 q^{93} - 95 q^{94} - 70 q^{96} + 390 q^{97} + 235 q^{98} + O(q^{100}) \)

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.