↑

Properties

Label 35.19
Level 35
Weight 19
Dimension 742
Nonzero newspaces 6
Sturm bound 1824
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(1824\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(35))\).

Total New Old
Modular forms 888 770 118
Cusp forms 840 742 98
Eisenstein series 48 28 20

Trace form

\( 742 q - 1026 q^{2} + 40254 q^{3} - 6 q^{4} - 4155237 q^{5} + 61533432 q^{6} - 113186236 q^{7} + 193084878 q^{8} - 1119729078 q^{9} + O(q^{10}) \) \( 742 q - 1026 q^{2} + 40254 q^{3} - 6 q^{4} - 4155237 q^{5} + 61533432 q^{6} - 113186236 q^{7} + 193084878 q^{8} - 1119729078 q^{9} - 946688972 q^{10} - 1046848818 q^{11} + 22429926540 q^{12} - 17378233892 q^{13} + 184531606002 q^{14} - 8840937174 q^{15} + 243113452102 q^{16} + 337273752930 q^{17} - 1893767075730 q^{18} - 1135813672734 q^{19} + 1756747016268 q^{20} + 1245003242754 q^{21} - 7746781136044 q^{22} - 6604073422482 q^{23} + 33679121665860 q^{24} + 783934752091 q^{25} - 25088593929072 q^{26} + 24640552855140 q^{27} + 46752632450866 q^{28} - 40746750709980 q^{29} + 204562088217396 q^{30} - 213319853920018 q^{31} + 370455188216562 q^{32} - 160089118337910 q^{33} - 81831168968043 q^{35} - 802795799292186 q^{36} - 565068456926750 q^{37} + 2456662351552836 q^{38} - 2829293755411044 q^{39} - 438649847164404 q^{40} + 2655207837364320 q^{41} + 2788639720939140 q^{42} - 6699047504510600 q^{43} - 71886866471784 q^{44} + 7784343577660002 q^{45} + 9539813942869364 q^{46} + 2129273612271078 q^{47} - 16570350335879724 q^{48} - 13295832888707934 q^{49} + 25852005932320026 q^{50} + 43153389698421966 q^{51} - 29089936695055892 q^{52} - 69604828767675246 q^{53} + 18719042990868564 q^{54} + 46862011018592924 q^{55} + 768471092525286 q^{56} - 56779410620734620 q^{57} - 40411155873191616 q^{58} - 17025741634654710 q^{59} + 53856242983607208 q^{60} + 96603816602591918 q^{61} - 10116972954893976 q^{62} + 48411153568925484 q^{63} - 185656718452815402 q^{64} + 83642488103895096 q^{65} + 531011780841306816 q^{66} + 65826138070473262 q^{67} - 668658669127258344 q^{68} - 25617039845728392 q^{70} - 286654245741973356 q^{71} - 799760188026108402 q^{72} - 170390750267237438 q^{73} + 892798599847021092 q^{74} + 911644518092450667 q^{75} - 885371022224425896 q^{76} - 708739976163189258 q^{77} + 318942127292776392 q^{78} + 1328478455028091242 q^{79} + 2389933972265391672 q^{80} - 2495004245370897864 q^{81} - 2383799418440597524 q^{82} - 528535486234195224 q^{83} + 3939952750214776668 q^{84} + 1199712358497438958 q^{85} - 934709801619190860 q^{86} + 322049391592596120 q^{87} - 5157068903962201392 q^{88} - 3975256352853882606 q^{89} - 695899484075384760 q^{90} + 4232623579443426076 q^{91} + 7249359120262902468 q^{92} + 4485614994109644618 q^{93} - 9972817012634393868 q^{94} - 4953644458388293233 q^{95} - 6193708087765596792 q^{96} + 4885936390985593492 q^{97} + 7327190337330505230 q^{98} + 8802292334826104484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.19.c \(\chi_{35}(34, \cdot)\) 35.19.c.a 1 1
35.19.c.b 1
35.19.c.c 68
35.19.d \(\chi_{35}(6, \cdot)\) 35.19.d.a 48 1
35.19.g \(\chi_{35}(8, \cdot)\) n/a 108 2
35.19.h \(\chi_{35}(26, \cdot)\) 35.19.h.a 96 2
35.19.i \(\chi_{35}(19, \cdot)\) n/a 140 2
35.19.l \(\chi_{35}(2, \cdot)\) n/a 280 4

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

Decomposition of \(S_{19}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{19}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{19}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)