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Properties

Label 272.10.y
Level $272$
Weight $10$
Character orbit 272.y
Rep. character $\chi_{272}(53,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1288$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.y (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

\( 1288 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 2052 q^{6} - 4 q^{8} + O(q^{10}) \) \( 1288 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 2052 q^{6} - 4 q^{8} + 2044 q^{10} - 4 q^{11} - 110664 q^{12} - 484600 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 1923544 q^{19} - 4 q^{20} - 3235148 q^{22} + 1556236 q^{24} - 8698996 q^{26} + 78728 q^{27} + 7280596 q^{28} - 4 q^{29} - 8 q^{31} - 1664684 q^{32} - 16 q^{33} - 2694420 q^{34} - 8 q^{35} - 36950372 q^{36} - 4 q^{37} - 4096 q^{38} + 17060904 q^{40} - 196458528 q^{42} - 8 q^{43} - 112146680 q^{44} - 7891236 q^{45} - 27916132 q^{46} + 153625104 q^{48} - 8 q^{49} - 8 q^{50} + 234714196 q^{51} - 8 q^{52} + 793253760 q^{54} + 585640000 q^{55} - 544707760 q^{56} - 157464 q^{57} - 2052 q^{58} - 8 q^{59} - 40082936 q^{60} + 180242204 q^{61} - 138752944 q^{62} - 8 q^{63} + 125612168 q^{65} + 1973953348 q^{66} - 8 q^{67} + 277913200 q^{68} - 8 q^{69} + 131313440 q^{70} + 283240 q^{72} + 11275124 q^{74} + 7891228 q^{75} - 1180207480 q^{76} + 222816936 q^{78} - 8 q^{79} + 1739876112 q^{80} + 39692564 q^{82} + 4957167432 q^{83} - 8 q^{84} - 4 q^{85} + 153559824 q^{86} + 1095115160 q^{88} - 4821599112 q^{90} - 1855922800 q^{91} - 1048580 q^{92} - 7355349400 q^{94} - 8 q^{95} + 769002656 q^{96} - 8 q^{97} - 11781731056 q^{98} - 1549760692 q^{99} + O(q^{100}) \)

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.