# Properties

 Label 289.10 Level 289 Weight 10 Dimension 30812 Nonzero newspaces 8 Sturm bound 69360 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$289 = 17^{2}$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$8$$ Sturm bound: $$69360$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(289))$$.

Total New Old
Modular forms 31412 31181 231
Cusp forms 31012 30812 200
Eisenstein series 400 369 31

## Trace form

 $$30812q - 120q^{2} - 120q^{3} - 120q^{4} - 120q^{5} - 120q^{6} - 120q^{7} - 120q^{8} - 120q^{9} + O(q^{10})$$ $$30812q - 120q^{2} - 120q^{3} - 120q^{4} - 120q^{5} - 120q^{6} - 120q^{7} - 120q^{8} - 120q^{9} + 61448q^{10} + 60136q^{11} + 896904q^{12} - 377912q^{13} - 970360q^{14} + 966888q^{15} + 3669912q^{16} + 308736q^{17} - 3734760q^{18} - 2220440q^{19} - 5146744q^{20} + 5152968q^{21} + 9744776q^{22} + 3092008q^{23} - 31925592q^{24} - 23681744q^{25} + 53035464q^{26} + 22989624q^{27} - 18741144q^{28} - 29258960q^{29} - 86147832q^{30} - 3271224q^{31} + 58890712q^{32} + 75898840q^{33} + 61465408q^{34} + 4108632q^{35} - 143599096q^{36} - 125996088q^{37} - 22140552q^{38} - 184533496q^{39} + 118666248q^{40} + 283562800q^{41} + 699835944q^{42} + 57512184q^{43} - 600146232q^{44} - 585225680q^{45} - 14224152q^{46} - 161098840q^{47} + 226946488q^{48} + 295934856q^{49} + 699999896q^{50} + 175275072q^{51} + 296091416q^{52} + 258939616q^{53} - 2153536344q^{54} - 1207313336q^{55} - 968574120q^{56} + 1187617272q^{57} + 1524503704q^{58} + 957680456q^{59} + 741133848q^{60} - 865028760q^{61} - 1574288552q^{62} - 2993135064q^{63} - 2391182360q^{64} + 572811200q^{65} + 5106267832q^{66} + 1289671640q^{67} + 2463221432q^{68} + 766638680q^{69} - 2677415528q^{70} - 1022236152q^{71} - 2038027048q^{72} - 657069120q^{73} - 519407448q^{74} - 2129717304q^{75} - 1235359688q^{76} + 690678760q^{77} + 4538331256q^{78} + 950835784q^{79} + 441706312q^{80} - 1001324936q^{81} - 1808591944q^{82} + 639284600q^{83} + 3095463608q^{84} + 1519695244q^{85} - 6712827656q^{86} + 2425871784q^{87} + 4564999176q^{88} + 5448594408q^{89} + 5470883816q^{90} - 4295066808q^{91} - 15068315928q^{92} - 9816863992q^{93} - 13901510712q^{94} - 8988123736q^{95} - 5156139848q^{96} + 5844004296q^{97} + 11728773368q^{98} + 14815111016q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(289))$$

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
289.10.a $$\chi_{289}(1, \cdot)$$ 289.10.a.a 5 1
289.10.a.b 7
289.10.a.c 12
289.10.a.d 12
289.10.a.e 12
289.10.a.f 24
289.10.a.g 36
289.10.a.h 36
289.10.a.i 52
289.10.b $$\chi_{289}(288, \cdot)$$ n/a 196 1
289.10.c $$\chi_{289}(38, \cdot)$$ n/a 392 2
289.10.d $$\chi_{289}(110, \cdot)$$ n/a 780 4
289.10.f $$\chi_{289}(18, \cdot)$$ n/a 3648 16
289.10.g $$\chi_{289}(16, \cdot)$$ n/a 3648 16
289.10.h $$\chi_{289}(4, \cdot)$$ n/a 7296 32
289.10.i $$\chi_{289}(2, \cdot)$$ n/a 14656 64

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

## Decomposition of $$S_{10}^{\mathrm{old}}(\Gamma_1(289))$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(\Gamma_1(289)) \cong$$ $$S_{10}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$