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Properties

Label 3100.3.ea
Level $3100$
Weight $3$
Character orbit 3100.ea
Rep. character $\chi_{3100}(939,\cdot)$
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.ea (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

\( 7648 q - 10 q^{2} - 2 q^{4} - 8 q^{5} + 25 q^{6} - 10 q^{8} - 11382 q^{9} + O(q^{10}) \) \( 7648 q - 10 q^{2} - 2 q^{4} - 8 q^{5} + 25 q^{6} - 10 q^{8} - 11382 q^{9} - 4 q^{10} - 10 q^{12} - 20 q^{13} - 25 q^{14} - 2 q^{16} - 20 q^{17} + 65 q^{18} - 24 q^{20} + 2 q^{21} - 85 q^{22} + 45 q^{24} - 32 q^{25} + 34 q^{26} - 15 q^{28} - 4 q^{29} - 53 q^{30} + 24 q^{34} + 18 q^{36} - 10 q^{37} + 10 q^{38} + 32 q^{40} - 16 q^{41} + 215 q^{42} + 75 q^{44} + 84 q^{45} + 20 q^{46} - 55 q^{48} + 6168 q^{49} + 647 q^{50} - 65 q^{52} + 340 q^{53} + 40 q^{54} + 5 q^{56} + 620 q^{58} + 447 q^{60} - 24 q^{61} + 30 q^{62} - 182 q^{64} + 82 q^{65} - 86 q^{66} + 165 q^{68} - 130 q^{69} - 631 q^{70} + 765 q^{72} - 30 q^{73} + 194 q^{74} + 170 q^{76} - 1000 q^{77} + 419 q^{80} - 33324 q^{81} - 23 q^{84} + 152 q^{85} + 605 q^{86} - 325 q^{88} - 24 q^{89} + 473 q^{90} + 1255 q^{92} + 930 q^{93} + 65 q^{94} + 90 q^{96} - 20 q^{97} - 250 q^{98} + O(q^{100}) \)

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.