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Properties

Label 140.6.o
Level $140$
Weight $6$
Character orbit 140.o
Rep. character $\chi_{140}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 140.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(140, [\chi])\).

Total New Old
Modular forms 248 160 88
Cusp forms 232 160 72
Eisenstein series 16 0 16

Trace form

\( 160 q - 2 q^{2} + 22 q^{4} - 356 q^{8} - 6480 q^{9} + O(q^{10}) \) \( 160 q - 2 q^{2} + 22 q^{4} - 356 q^{8} - 6480 q^{9} - 3270 q^{12} - 2250 q^{14} - 1710 q^{16} + 3200 q^{18} + 9316 q^{21} - 27672 q^{22} + 324 q^{24} + 50000 q^{25} + 17970 q^{26} - 9382 q^{28} - 8328 q^{29} + 2498 q^{32} + 29740 q^{36} - 23448 q^{37} - 29940 q^{38} - 91058 q^{42} - 3050 q^{44} - 17700 q^{45} - 23690 q^{46} - 56656 q^{49} - 2500 q^{50} + 55116 q^{52} + 66968 q^{53} - 7260 q^{54} + 85532 q^{56} - 77328 q^{57} - 28562 q^{58} - 3850 q^{60} - 37704 q^{61} + 69124 q^{64} - 21100 q^{65} - 393240 q^{66} + 241740 q^{68} + 62900 q^{70} - 205884 q^{72} + 473112 q^{73} - 19766 q^{74} + 92280 q^{77} - 50520 q^{78} - 636980 q^{81} + 406518 q^{82} + 570748 q^{84} + 385364 q^{86} + 28676 q^{88} + 23700 q^{89} + 29964 q^{92} + 333848 q^{93} - 336762 q^{94} - 1368348 q^{96} - 477198 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(140, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)