↑

Properties

Label 272.10.w
Level $272$
Weight $10$
Character orbit 272.w
Rep. character $\chi_{272}(189,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1288$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(272, [\chi])\).

Total New Old
Modular forms 1304 1304 0
Cusp forms 1288 1288 0
Eisenstein series 16 16 0

Trace form

\( 1288 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 2044 q^{6} - 4 q^{8} + O(q^{10}) \) \( 1288 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 2044 q^{6} - 4 q^{8} - 2052 q^{10} - 4 q^{11} + 110656 q^{12} + 926800 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} - 3239244 q^{22} + 17164612 q^{24} + 8698988 q^{26} - 78736 q^{27} - 18748268 q^{28} - 4 q^{29} - 8 q^{31} - 27776644 q^{32} - 16 q^{33} + 2694412 q^{34} - 8 q^{35} - 36950372 q^{36} - 4 q^{37} + 4096 q^{38} - 122474096 q^{40} - 28100560 q^{42} - 61671280 q^{44} + 7891228 q^{45} - 27916132 q^{46} + 286993872 q^{48} - 8 q^{49} - 8 q^{50} + 234714196 q^{51} - 8 q^{52} - 8 q^{53} - 147021512 q^{54} - 585640000 q^{55} + 89708592 q^{56} + 157464 q^{57} + 2044 q^{58} + 42180080 q^{60} + 180242204 q^{61} + 138752936 q^{62} - 8 q^{63} + 125612168 q^{65} + 292829228 q^{66} - 8 q^{67} + 158108224 q^{68} - 8 q^{69} - 131313448 q^{70} - 283240 q^{72} + 11271028 q^{74} - 7891236 q^{75} - 1545289168 q^{76} - 8 q^{77} - 3442660256 q^{78} - 8 q^{79} + 1739876112 q^{80} - 39692572 q^{82} - 8 q^{84} - 4 q^{85} + 153559824 q^{86} - 2346295560 q^{88} - 2459635016 q^{90} + 1533093936 q^{91} - 1048580 q^{92} - 8 q^{93} - 1278783976 q^{94} - 8 q^{95} - 769002664 q^{96} - 8 q^{97} + 11781731056 q^{98} + 1549603220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(272, [\chi])\) into newform subspaces

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