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Properties

Label 272.10.r
Level $272$
Weight $10$
Character orbit 272.r
Rep. character $\chi_{272}(101,\cdot)$
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.r (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

\( 644 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + O(q^{10}) \) \( 644 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{13} - 810008 q^{15} - 1068412 q^{16} - 4 q^{17} - 2124976 q^{18} - 961780 q^{19} - 78736 q^{21} - 4 q^{26} - 11067872 q^{30} - 468524 q^{32} - 8 q^{33} + 4526152 q^{34} - 7812504 q^{35} - 62478400 q^{36} - 10145052 q^{38} + 71968752 q^{42} - 4 q^{43} + 195187232 q^{47} + 3574176612 q^{49} - 114974584 q^{50} - 207332064 q^{51} - 261806044 q^{52} - 4 q^{53} - 288075236 q^{59} - 251393800 q^{60} - 341202460 q^{64} - 1179897816 q^{66} - 4 q^{67} + 67746768 q^{68} + 764641616 q^{69} + 563675568 q^{70} - 2134144480 q^{72} + 1807103804 q^{76} - 161414432 q^{77} - 26344593260 q^{81} - 2478583724 q^{83} - 381961232 q^{84} - 425303752 q^{85} - 2745326460 q^{86} + 78728 q^{93} - 4052320528 q^{94} - 767253964 q^{98} + O(q^{100}) \)

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.