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Properties

Label 272.10.j
Level $272$
Weight $10$
Character orbit 272.j
Rep. character $\chi_{272}(13,\cdot)$
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.j (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

\( 644 q - 4 q^{4} - 4 q^{5} + 7178 q^{6} - 4172796 q^{9} + O(q^{10}) \) \( 644 q - 4 q^{4} - 4 q^{5} + 7178 q^{6} - 4172796 q^{9} - 23526 q^{10} + 94694 q^{12} - 4 q^{13} + 241272 q^{14} + 1068404 q^{16} - 4 q^{17} - 2052 q^{18} + 380710 q^{20} - 4 q^{21} + 1619618 q^{22} + 2612538 q^{24} + 245312500 q^{25} - 5823500 q^{26} - 13773428 q^{28} + 11067864 q^{30} - 4 q^{31} + 16262380 q^{32} - 8 q^{33} - 17699638 q^{34} - 4 q^{35} + 78732 q^{36} - 4 q^{37} - 4 q^{38} + 78732 q^{39} - 89399374 q^{40} - 30221888 q^{42} + 23165554 q^{44} - 7733772 q^{45} + 44499644 q^{46} - 195187248 q^{47} - 188126806 q^{48} - 2052 q^{50} - 207332064 q^{51} + 12613748 q^{52} + 224955176 q^{54} - 65974064 q^{56} + 78732 q^{57} + 260779838 q^{58} - 288075232 q^{59} + 643481092 q^{60} - 180242212 q^{61} + 28814132 q^{62} - 161414432 q^{63} + 341202452 q^{64} + 62806084 q^{65} + 434619756 q^{66} - 4 q^{67} - 338508298 q^{68} - 764720356 q^{69} + 545822500 q^{70} - 536870916 q^{72} + 241709752 q^{73} - 999119894 q^{74} - 1817323056 q^{76} + 161414428 q^{77} + 3804653996 q^{78} - 1134564340 q^{79} + 222343214 q^{80} + 26344593244 q^{81} - 221824424 q^{82} - 4 q^{84} - 433116252 q^{85} - 2250912280 q^{86} - 2749751064 q^{87} + 1081283190 q^{88} - 1811285254 q^{90} + 1902807584 q^{92} + 78732 q^{93} - 1494195336 q^{94} - 4 q^{95} + 2316185598 q^{96} - 4 q^{97} - 1271928640 q^{98} + O(q^{100}) \)

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.