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Properties

Label 3100.3.bi
Level $3100$
Weight $3$
Character orbit 3100.bi
Rep. character $\chi_{3100}(1039,\cdot)$
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.bi (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

\( 3824 q - 5 q^{2} - q^{4} - 16 q^{5} - 10 q^{6} - 5 q^{8} - 2846 q^{9} + O(q^{10}) \) \( 3824 q - 5 q^{2} - q^{4} - 16 q^{5} - 10 q^{6} - 5 q^{8} - 2846 q^{9} - 20 q^{10} - 10 q^{13} - 15 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} + 35 q^{20} + 70 q^{21} - 15 q^{24} - 32 q^{25} - 142 q^{26} - 5 q^{28} - 2 q^{29} + 28 q^{30} - 40 q^{33} - 17 q^{34} + 19 q^{36} - 20 q^{37} + 160 q^{38} - 131 q^{40} - 12 q^{41} + 75 q^{44} + 178 q^{45} + 15 q^{46} - 5 q^{48} - 6376 q^{49} - 158 q^{50} + 130 q^{52} + 190 q^{54} - 235 q^{56} - 207 q^{60} - 12 q^{61} - 230 q^{62} - 91 q^{64} - 106 q^{65} - 110 q^{66} - 600 q^{69} + 315 q^{70} - 305 q^{72} - 10 q^{73} + 53 q^{74} + 160 q^{76} + 40 q^{78} - 950 q^{80} - 8336 q^{81} - 565 q^{82} + 50 q^{84} - 74 q^{85} - 585 q^{86} - 825 q^{88} - 2 q^{89} - 38 q^{90} - 355 q^{92} - 95 q^{94} - 70 q^{96} - 10 q^{97} + 10 q^{98} + O(q^{100}) \)

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.