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Properties

Label 272.10.s
Level $272$
Weight $10$
Character orbit 272.s
Rep. character $\chi_{272}(149,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $644$
Sturm bound $360$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 652 652 0
Cusp forms 644 644 0
Eisenstein series 8 8 0

Trace form

\( 644 q - 4 q^{3} - 4 q^{4} - 7182 q^{6} + 4172796 q^{9} + O(q^{10}) \) \( 644 q - 4 q^{3} - 4 q^{4} - 7182 q^{6} + 4172796 q^{9} - 21478 q^{10} - 4 q^{11} - 94698 q^{12} - 4 q^{13} - 464428 q^{14} + 1068404 q^{16} - 4 q^{17} - 2052 q^{18} + 1429286 q^{20} - 4 q^{21} + 1617570 q^{22} - 5349114 q^{24} - 245312500 q^{25} + 5823500 q^{26} - 78736 q^{27} - 758996 q^{28} - 4 q^{29} + 11067864 q^{30} - 4 q^{31} - 16262380 q^{32} - 8 q^{33} + 17701682 q^{34} - 4 q^{35} - 78732 q^{36} - 4 q^{38} - 78732 q^{39} + 36692778 q^{40} + 30221888 q^{42} - 3120722 q^{44} - 19532188 q^{46} - 195187248 q^{47} - 254889922 q^{48} - 2052 q^{50} - 27382140 q^{51} + 12613748 q^{52} - 588382092 q^{54} + 132059212 q^{56} - 78732 q^{57} + 99571226 q^{58} + 288075232 q^{59} - 643481092 q^{60} + 269994704 q^{62} - 161414432 q^{63} + 341202452 q^{64} + 62806084 q^{65} - 434619756 q^{66} - 4 q^{67} + 120497578 q^{68} - 764720356 q^{69} - 545822500 q^{70} - 536870916 q^{72} - 241709752 q^{73} - 362339646 q^{74} + 7733764 q^{75} + 1817323056 q^{76} - 161414428 q^{77} - 381405108 q^{78} - 1134564340 q^{79} - 616947354 q^{80} + 26344593244 q^{81} + 355695612 q^{82} - 4 q^{84} + 433116248 q^{85} - 2250912280 q^{86} + 2749751064 q^{87} + 473843782 q^{88} - 7426035634 q^{90} - 3716227544 q^{91} - 2518336768 q^{92} - 78732 q^{93} + 1494195336 q^{94} - 4 q^{95} + 2867105218 q^{96} - 4 q^{97} - 1271928640 q^{98} - 1549760692 q^{99} + O(q^{100}) \)

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.