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Properties

Label 3100.3.bg
Level $3100$
Weight $3$
Character orbit 3100.bg
Rep. character $\chi_{3100}(779,\cdot)$
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.bg (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

\( 3824 q - 6 q^{4} - 16 q^{5} - 10 q^{6} - 2846 q^{9} + O(q^{10}) \) \( 3824 q - 6 q^{4} - 16 q^{5} - 10 q^{6} - 2846 q^{9} + 45 q^{10} - 5 q^{12} + 40 q^{14} - 6 q^{16} + 20 q^{18} - 20 q^{20} - 20 q^{21} + 70 q^{22} - 15 q^{24} - 32 q^{25} - 142 q^{26} + 155 q^{28} - 2 q^{29} + 28 q^{30} + 20 q^{33} + 18 q^{34} + 19 q^{36} - 20 q^{37} - 45 q^{38} + 204 q^{40} - 2 q^{41} + 205 q^{42} + 60 q^{44} + 58 q^{45} - 25 q^{46} + 85 q^{48} - 6376 q^{49} - 413 q^{50} - 10 q^{53} - 25 q^{54} - 235 q^{56} + 35 q^{58} - 222 q^{60} - 12 q^{61} - 350 q^{62} - 96 q^{64} + 144 q^{65} - 160 q^{66} + 790 q^{69} - 110 q^{70} + 590 q^{72} - 10 q^{73} + 53 q^{74} + 160 q^{76} - 10 q^{77} + 220 q^{78} + 410 q^{80} - 8336 q^{81} + 565 q^{82} + 135 q^{84} + 96 q^{85} + 125 q^{86} - 825 q^{88} - 2 q^{89} - 1263 q^{90} - 355 q^{92} - 95 q^{94} - 70 q^{96} + 10 q^{98} + O(q^{100}) \)

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.