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Properties

Label 3100.3.bc
Level $3100$
Weight $3$
Character orbit 3100.bc
Rep. character $\chi_{3100}(411,\cdot)$
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.bc (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

\( 3824 q - q^{2} - q^{4} - 16 q^{5} - 2 q^{6} + 5 q^{8} - 11388 q^{9} + O(q^{10}) \) \( 3824 q - q^{2} - q^{4} - 16 q^{5} - 2 q^{6} + 5 q^{8} - 11388 q^{9} + 14 q^{10} + 53 q^{12} - 2 q^{13} + 48 q^{14} - q^{16} - 2 q^{17} - q^{18} + 18 q^{20} + 16 q^{21} + 8 q^{22} + 3 q^{24} - 40 q^{25} - 100 q^{26} - 286 q^{28} - 2 q^{29} + 91 q^{30} - 276 q^{32} + 240 q^{33} - 5 q^{34} + 187 q^{36} - 12 q^{37} + 131 q^{38} + 95 q^{40} - 2 q^{41} + 340 q^{42} + 60 q^{44} - 60 q^{45} - 22 q^{46} + 53 q^{48} + 6472 q^{49} + 1071 q^{50} + 10 q^{52} - 74 q^{53} + 41 q^{54} - 22 q^{56} + 76 q^{57} + 393 q^{58} - 68 q^{60} - 12 q^{61} + 95 q^{62} - 91 q^{64} + 94 q^{65} + 140 q^{66} + 444 q^{68} - 464 q^{69} - 315 q^{70} + 159 q^{72} - 236 q^{73} - 210 q^{74} - 140 q^{76} + 586 q^{77} + 176 q^{78} + 438 q^{80} + 33360 q^{81} + 220 q^{82} + 6 q^{84} + 62 q^{85} + 578 q^{86} + 454 q^{88} - 12 q^{89} - 163 q^{90} - 192 q^{92} - 850 q^{93} - 127 q^{94} + 288 q^{96} + 158 q^{97} - 553 q^{98} + O(q^{100}) \)

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.