# Properties

 Label 140.6 Level 140 Weight 6 Dimension 1446 Nonzero newspaces 12 Sturm bound 6912 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$12$$ Sturm bound: $$6912$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(140))$$.

Total New Old
Modular forms 3000 1502 1498
Cusp forms 2760 1446 1314
Eisenstein series 240 56 184

## Trace form

 $$1446 q - 2 q^{2} - 26 q^{3} - 6 q^{4} + 93 q^{5} + 344 q^{6} + 14 q^{7} - 1034 q^{8} - 478 q^{9} + O(q^{10})$$ $$1446 q - 2 q^{2} - 26 q^{3} - 6 q^{4} + 93 q^{5} + 344 q^{6} + 14 q^{7} - 1034 q^{8} - 478 q^{9} - 340 q^{10} + 826 q^{11} - 716 q^{12} + 1592 q^{13} - 3726 q^{14} + 1198 q^{15} - 1690 q^{16} - 746 q^{17} + 19974 q^{18} - 794 q^{19} + 2716 q^{20} + 11894 q^{21} - 21556 q^{22} + 10002 q^{23} - 1140 q^{24} + 9233 q^{25} + 4088 q^{26} - 11576 q^{27} + 27722 q^{28} - 54156 q^{29} - 22576 q^{30} - 19494 q^{31} - 52022 q^{32} + 40646 q^{33} + 19879 q^{35} + 75790 q^{36} + 16186 q^{37} + 55612 q^{38} - 61648 q^{39} + 27824 q^{40} - 2996 q^{41} - 22124 q^{42} - 28196 q^{43} - 40200 q^{44} - 50144 q^{45} - 91340 q^{46} + 7446 q^{47} - 216332 q^{48} + 102654 q^{49} - 139470 q^{50} + 53774 q^{51} + 58876 q^{52} + 25630 q^{53} + 155292 q^{54} + 3442 q^{55} + 189142 q^{56} - 103852 q^{57} + 300096 q^{58} + 45658 q^{59} + 116068 q^{60} - 175574 q^{61} - 91064 q^{62} + 139546 q^{63} - 211290 q^{64} - 24298 q^{65} - 433320 q^{66} + 65998 q^{67} - 94456 q^{68} + 279604 q^{69} + 319640 q^{70} - 408 q^{71} - 540690 q^{72} + 370430 q^{73} - 463020 q^{74} + 30323 q^{75} + 163896 q^{76} + 168258 q^{77} + 696984 q^{78} - 118802 q^{79} + 348968 q^{80} - 815964 q^{81} + 946468 q^{82} - 275868 q^{83} + 1242108 q^{84} + 45878 q^{85} + 243820 q^{86} - 1440 q^{87} - 588976 q^{88} + 57398 q^{89} - 1797432 q^{90} + 490204 q^{91} - 1731532 q^{92} + 843838 q^{93} - 719988 q^{94} + 677689 q^{95} - 439528 q^{96} - 600320 q^{97} - 653506 q^{98} - 558952 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(140))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
140.6.a $$\chi_{140}(1, \cdot)$$ 140.6.a.a 2 1
140.6.a.b 2
140.6.a.c 3
140.6.a.d 3
140.6.c $$\chi_{140}(139, \cdot)$$ n/a 116 1
140.6.e $$\chi_{140}(29, \cdot)$$ 140.6.e.a 16 1
140.6.g $$\chi_{140}(111, \cdot)$$ 140.6.g.a 80 1
140.6.i $$\chi_{140}(81, \cdot)$$ 140.6.i.a 2 2
140.6.i.b 4
140.6.i.c 8
140.6.i.d 14
140.6.k $$\chi_{140}(43, \cdot)$$ n/a 180 2
140.6.m $$\chi_{140}(13, \cdot)$$ 140.6.m.a 40 2
140.6.o $$\chi_{140}(31, \cdot)$$ n/a 160 2
140.6.q $$\chi_{140}(9, \cdot)$$ 140.6.q.a 40 2
140.6.s $$\chi_{140}(19, \cdot)$$ n/a 232 2
140.6.u $$\chi_{140}(17, \cdot)$$ 140.6.u.a 80 4
140.6.w $$\chi_{140}(23, \cdot)$$ n/a 464 4

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(140))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(140)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 2}$$