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Properties

Label 140.6.w
Level $140$
Weight $6$
Character orbit 140.w
Rep. character $\chi_{140}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $464$
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.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(144\)

Dimensions

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

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 2 q^{2} - 4 q^{5} - 16 q^{6} - 500 q^{8} + O(q^{10}) \) \( 464 q - 2 q^{2} - 4 q^{5} - 16 q^{6} - 500 q^{8} - 2 q^{10} + 970 q^{12} - 16 q^{13} + 756 q^{16} - 4 q^{17} + 356 q^{18} - 4104 q^{20} - 1656 q^{21} - 136 q^{22} - 4 q^{25} - 11924 q^{26} + 27722 q^{28} - 22472 q^{30} - 4822 q^{32} + 7484 q^{33} - 8208 q^{36} - 4 q^{37} + 13872 q^{38} - 29622 q^{40} + 19248 q^{41} + 45870 q^{42} - 25004 q^{45} - 22924 q^{46} - 90548 q^{48} + 38916 q^{50} - 74656 q^{52} - 4 q^{53} + 100612 q^{56} + 84520 q^{57} + 27862 q^{58} - 19650 q^{60} - 8 q^{61} - 206704 q^{62} + 23980 q^{65} - 70100 q^{66} + 93164 q^{68} + 57944 q^{70} + 110956 q^{72} - 13140 q^{73} - 279344 q^{76} + 53268 q^{77} + 78784 q^{78} - 131484 q^{80} + 878040 q^{81} + 49894 q^{82} - 31648 q^{85} + 132936 q^{86} - 8144 q^{88} - 606536 q^{90} - 342196 q^{92} - 364 q^{93} - 125424 q^{96} - 660896 q^{97} + 221162 q^{98} + O(q^{100}) \)

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.