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Properties

Label 289.10.f
Level $289$
Weight $10$
Character orbit 289.f
Rep. character $\chi_{289}(18,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $3648$
Sturm bound $255$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.f (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{17})\)
Sturm bound: \(255\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(289, [\chi])\).

Total New Old
Modular forms 3680 3680 0
Cusp forms 3648 3648 0
Eisenstein series 32 32 0

Trace form

\( 3648 q + 17 q^{2} + 131 q^{3} - 58555 q^{4} + 16487 q^{5} + 4125 q^{6} + 3797 q^{7} + 25585 q^{8} - 1509593 q^{9} + O(q^{10}) \) \( 3648 q + 17 q^{2} + 131 q^{3} - 58555 q^{4} + 16487 q^{5} + 4125 q^{6} + 3797 q^{7} + 25585 q^{8} - 1509593 q^{9} + 126335 q^{10} - 67517 q^{11} + 207833 q^{12} - 25349 q^{13} + 2636656 q^{14} + 627727 q^{15} - 8426567 q^{16} - 167059 q^{17} + 1995949 q^{18} - 631089 q^{19} - 715495 q^{20} - 3375473 q^{21} + 1100213 q^{22} - 3003651 q^{23} - 26897484 q^{24} - 102099475 q^{25} + 11807983 q^{26} - 16909288 q^{27} + 3145503 q^{28} - 4635635 q^{29} - 10022479 q^{30} + 3715605 q^{31} + 8911631 q^{32} - 75563425 q^{33} - 2672689 q^{34} + 26777903 q^{35} - 403301625 q^{36} + 13124193 q^{37} - 24434138 q^{38} - 162366997 q^{39} - 73224632 q^{40} - 2288765 q^{41} + 16253969 q^{42} + 52682071 q^{43} - 205578223 q^{44} - 107898023 q^{45} - 126255733 q^{46} - 106952799 q^{47} - 632122364 q^{48} - 1256123565 q^{49} + 74923219 q^{50} - 688810845 q^{51} + 6616239 q^{52} + 281006963 q^{53} + 38078068 q^{54} + 49078871 q^{55} - 121233953 q^{56} - 290228881 q^{57} - 1211179404 q^{58} - 42880505 q^{59} + 828485005 q^{60} + 127601281 q^{61} + 1264725383 q^{62} - 868816993 q^{63} - 4244025063 q^{64} + 162954922 q^{65} + 5316111598 q^{66} + 332303648 q^{67} - 128288273 q^{68} + 2521669367 q^{69} - 650853229 q^{70} + 836060221 q^{71} + 484000875 q^{72} - 16675873 q^{73} + 4665641260 q^{74} - 783077870 q^{75} - 849772877 q^{76} - 2501628135 q^{77} - 1015080629 q^{78} + 1080496627 q^{79} - 6329611033 q^{80} - 7034206805 q^{81} + 63174383 q^{82} + 7890988999 q^{83} - 595364725 q^{84} + 4737134031 q^{85} - 580202211 q^{86} + 1037810283 q^{87} - 17360677071 q^{88} + 1536071595 q^{89} + 4524752117 q^{90} + 162231351 q^{91} - 10965008835 q^{92} - 2583172645 q^{93} - 770683611 q^{94} + 1750951631 q^{95} - 13315241616 q^{96} - 2698561517 q^{97} + 19490033583 q^{98} + 552052847 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(289, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.