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Properties

Label 140.15
Level 140
Weight 15
Dimension 4112
Nonzero newspaces 12
Sturm bound 17280
Trace bound 2

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Defining parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(17280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(140))\).

Total New Old
Modular forms 8184 4176 4008
Cusp forms 7944 4112 3832
Eisenstein series 240 64 176

Trace form

\( 4112 q - 370 q^{2} - 58 q^{3} - 5566 q^{4} + 47799 q^{5} + 430580 q^{6} + 784246 q^{7} + 12095042 q^{8} - 17499068 q^{9} + O(q^{10}) \) \( 4112 q - 370 q^{2} - 58 q^{3} - 5566 q^{4} + 47799 q^{5} + 430580 q^{6} + 784246 q^{7} + 12095042 q^{8} - 17499068 q^{9} - 9933774 q^{10} - 68262002 q^{11} + 265541704 q^{12} - 473256268 q^{13} + 31838938 q^{14} + 1410787142 q^{15} + 69928902 q^{16} - 2064421550 q^{17} - 742984646 q^{18} - 824163030 q^{19} - 3407858924 q^{20} - 1032940534 q^{21} + 9376314232 q^{22} - 28019760014 q^{23} - 6077601384 q^{24} - 65037950255 q^{25} + 34308602832 q^{26} - 45520009732 q^{27} + 57211153522 q^{28} + 32553910016 q^{29} - 68839014614 q^{30} + 73035730442 q^{31} - 92998920770 q^{32} - 430871043710 q^{33} + 767491412148 q^{34} - 74331990385 q^{35} - 880376782690 q^{36} - 782729540254 q^{37} - 455111130308 q^{38} + 1631901454932 q^{39} + 1101888957504 q^{40} + 705674855480 q^{41} - 3621334128216 q^{42} - 785369290220 q^{43} - 260358607252 q^{44} + 1193988796790 q^{45} + 2161579304924 q^{46} + 566797815786 q^{47} - 422355863880 q^{48} + 6385422656236 q^{49} - 2828362569770 q^{50} + 6428500727890 q^{51} - 37739767876 q^{52} - 12012189685154 q^{53} + 3633090577624 q^{54} + 8323061153064 q^{55} - 8756225502358 q^{56} + 11943730809596 q^{57} + 12219479990952 q^{58} - 4348847262006 q^{59} - 12525649198844 q^{60} - 8700192936850 q^{61} + 42976152832160 q^{62} + 9228191001670 q^{63} - 10024181468986 q^{64} - 11417083764880 q^{65} - 11457299686300 q^{66} - 37292331368574 q^{67} + 5767338382636 q^{68} + 116703676474648 q^{69} + 61524607937174 q^{70} + 25284626518664 q^{71} + 89227828665090 q^{72} - 101358206938270 q^{73} + 7936545723648 q^{74} - 46838605639679 q^{75} + 35224634774388 q^{76} + 22138744573222 q^{77} - 38194165893752 q^{78} + 78977201282966 q^{79} + 186517248371552 q^{80} - 288132243290406 q^{81} - 285729641303728 q^{82} - 100172447022756 q^{83} + 44298691240912 q^{84} + 148053184381738 q^{85} + 335507948527136 q^{86} + 336572501367080 q^{87} + 415182177635572 q^{88} + 393345905050114 q^{89} - 800913804808764 q^{90} - 350298041095860 q^{91} - 172648864781784 q^{92} + 991640410023730 q^{93} + 610744197554392 q^{94} + 571860753750509 q^{95} - 131773110511660 q^{96} + 456622020197100 q^{97} - 738172855367570 q^{98} - 822391428627888 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(140))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
140.15.b \(\chi_{140}(71, \cdot)\) n/a 168 1
140.15.d \(\chi_{140}(41, \cdot)\) 140.15.d.a 36 1
140.15.f \(\chi_{140}(99, \cdot)\) n/a 252 1
140.15.h \(\chi_{140}(69, \cdot)\) 140.15.h.a 2 1
140.15.h.b 2
140.15.h.c 52
140.15.j \(\chi_{140}(27, \cdot)\) n/a 664 2
140.15.l \(\chi_{140}(57, \cdot)\) 140.15.l.a 84 2
140.15.n \(\chi_{140}(89, \cdot)\) n/a 112 2
140.15.p \(\chi_{140}(39, \cdot)\) n/a 664 2
140.15.r \(\chi_{140}(61, \cdot)\) 140.15.r.a 76 2
140.15.t \(\chi_{140}(11, \cdot)\) n/a 448 2
140.15.v \(\chi_{140}(37, \cdot)\) n/a 224 4
140.15.x \(\chi_{140}(3, \cdot)\) n/a 1328 4

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

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(140)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)