Properties

Label 289.10.i
Level $289$
Weight $10$
Character orbit 289.i
Rep. character $\chi_{289}(2,\cdot)$
Character field $\Q(\zeta_{136})$
Dimension $14656$
Sturm bound $255$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.i (of order \(136\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{136})\)
Sturm bound: \(255\)

Dimensions

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

Total New Old
Modular forms 14784 14784 0
Cusp forms 14656 14656 0
Eisenstein series 128 128 0

Trace form

\( 14656 q - 64 q^{2} - 64 q^{3} - 68 q^{4} + 1072 q^{5} - 12376 q^{6} - 64 q^{7} - 2112 q^{8} + 83156 q^{9} + O(q^{10}) \) \( 14656 q - 64 q^{2} - 64 q^{3} - 68 q^{4} + 1072 q^{5} - 12376 q^{6} - 64 q^{7} - 2112 q^{8} + 83156 q^{9} + 117568 q^{10} + 115700 q^{11} + 145460 q^{12} - 68 q^{13} - 463728 q^{14} - 288312 q^{15} + 60030916 q^{16} + 271864 q^{17} - 1259772 q^{18} + 406632 q^{19} - 493632 q^{20} - 68 q^{21} - 801032 q^{22} + 4172112 q^{23} + 87745992 q^{24} - 11946644 q^{25} + 14208944 q^{26} + 7973588 q^{27} - 13540872 q^{28} - 7833820 q^{29} - 68 q^{30} - 5936320 q^{31} + 26730048 q^{32} + 18974676 q^{33} + 53493920 q^{34} - 48020060 q^{35} + 12761696 q^{36} - 74606864 q^{37} + 399943124 q^{39} + 69317604 q^{40} + 71362220 q^{41} + 308117596 q^{42} + 3765644 q^{43} - 163659888 q^{44} - 14167476 q^{45} - 72135496 q^{46} - 68 q^{47} - 164621480 q^{48} + 284548440 q^{49} + 174999940 q^{50} + 406733064 q^{51} - 177575996 q^{52} + 244724660 q^{53} + 4521747848 q^{54} - 68 q^{55} - 470691720 q^{56} + 440646512 q^{57} + 308561700 q^{58} + 481734916 q^{59} - 379626244 q^{60} - 507966296 q^{61} - 6423163880 q^{62} - 1070586524 q^{63} - 68 q^{64} - 366263752 q^{65} + 2244715080 q^{66} + 322417876 q^{67} + 1839196600 q^{68} - 725347932 q^{69} - 34867740 q^{70} - 186006880 q^{71} - 68 q^{72} - 487115260 q^{73} + 214149344 q^{74} - 533015988 q^{75} - 1104202164 q^{76} + 12668568904 q^{77} + 2081523316 q^{78} + 136337984 q^{79} + 922534084 q^{80} - 68 q^{81} - 1951892452 q^{82} - 1843663956 q^{83} + 771768716 q^{84} + 18553481348 q^{85} + 139659492 q^{86} + 369395568 q^{87} + 3388839572 q^{88} - 68 q^{89} - 874363752 q^{90} - 2087197788 q^{91} + 3984524944 q^{92} - 576415488 q^{93} - 6899365180 q^{94} - 5031766944 q^{95} - 490811432 q^{96} + 3419996300 q^{97} - 68 q^{98} + 5630536044 q^{99} + O(q^{100}) \)

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

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