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Properties

Label 3100.3.bu
Level $3100$
Weight $3$
Character orbit 3100.bu
Rep. character $\chi_{3100}(311,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $3600$
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
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 3600 256
Cusp forms 3824 3600 224
Eisenstein series 32 0 32

Trace form

\( 3600 q + 4 q^{5} + 9 q^{8} + 2700 q^{9} + O(q^{10}) \) \( 3600 q + 4 q^{5} + 9 q^{8} + 2700 q^{9} - q^{10} + 48 q^{12} - 24 q^{13} + 30 q^{14} + 120 q^{16} - 40 q^{17} + 28 q^{18} + 63 q^{20} - 112 q^{22} - 140 q^{24} + 60 q^{25} - 86 q^{28} + 40 q^{29} + 166 q^{30} + 160 q^{34} - 60 q^{37} - 279 q^{38} + 180 q^{40} - 200 q^{41} - 120 q^{42} - 60 q^{45} + 200 q^{46} + 98 q^{48} - 25200 q^{49} - 39 q^{50} - 628 q^{52} + 84 q^{53} - 390 q^{54} - 64 q^{57} - 424 q^{58} + 802 q^{60} + 200 q^{61} - 375 q^{64} + 444 q^{65} - 240 q^{66} - 468 q^{68} - 165 q^{70} - 135 q^{72} + 312 q^{73} - 420 q^{74} - 150 q^{76} + 96 q^{77} + 1366 q^{78} - 527 q^{80} - 7620 q^{81} - 898 q^{82} - 1100 q^{84} + 452 q^{85} - 300 q^{86} - 856 q^{88} + 780 q^{89} - 288 q^{90} - 192 q^{92} - 480 q^{94} - 1280 q^{96} - 360 q^{97} + 486 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{3}^{\mathrm{old}}(3100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)