Properties

Label 140.6.k
Level $140$
Weight $6$
Character orbit 140.k
Rep. character $\chi_{140}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $180$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(144\)

Dimensions

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

Total New Old
Modular forms 248 180 68
Cusp forms 232 180 52
Eisenstein series 16 0 16

Trace form

\( 180 q + 360 q^{6} + O(q^{10}) \) \( 180 q + 360 q^{6} - 1136 q^{10} + 1584 q^{12} - 244 q^{13} - 2440 q^{16} - 2020 q^{17} + 7588 q^{18} + 6820 q^{20} + 5004 q^{22} + 15580 q^{25} - 1760 q^{26} - 13484 q^{30} - 30400 q^{32} + 64000 q^{36} + 18820 q^{37} + 71680 q^{38} + 3644 q^{40} + 40180 q^{42} - 30780 q^{45} - 35920 q^{46} - 125784 q^{48} - 81960 q^{50} + 78416 q^{52} + 117956 q^{53} + 64680 q^{56} - 41296 q^{57} + 193316 q^{58} + 276040 q^{60} - 192320 q^{61} + 115640 q^{62} + 112404 q^{65} - 17440 q^{66} - 429360 q^{68} - 235120 q^{72} - 65468 q^{73} + 443240 q^{76} + 546044 q^{78} + 635180 q^{80} - 1180980 q^{81} + 490056 q^{82} + 86780 q^{85} - 274520 q^{86} - 708200 q^{88} - 1190896 q^{90} - 811416 q^{92} - 364128 q^{93} + 894200 q^{96} + 402020 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)