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Properties

Label 272.10.o
Level $272$
Weight $10$
Character orbit 272.o
Rep. character $\chi_{272}(81,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
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 660 164 496
Cusp forms 636 160 476
Eisenstein series 24 4 20

Trace form

\( 160 q + 2 q^{3} + 716 q^{5} + 2 q^{7} + O(q^{10}) \) \( 160 q + 2 q^{3} + 716 q^{5} + 2 q^{7} + 2 q^{11} - 4 q^{13} - 102000 q^{17} - 4 q^{21} - 2753266 q^{23} - 39364 q^{27} - 1063440 q^{29} - 6344710 q^{31} + 19208628 q^{33} - 36014996 q^{35} - 1602812 q^{37} - 57311776 q^{39} - 2180784 q^{41} - 19608376 q^{45} - 97593616 q^{47} - 577682 q^{51} - 103432716 q^{55} - 89669948 q^{57} - 380458116 q^{61} + 291491458 q^{63} - 154314260 q^{65} - 176980832 q^{67} - 594500436 q^{69} + 628634142 q^{71} + 133128312 q^{73} + 485933710 q^{75} - 19603090 q^{79} - 6108128988 q^{81} - 25514976 q^{85} - 4 q^{89} - 766546968 q^{91} + 3533776348 q^{95} - 155690628 q^{97} - 1895509246 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{10}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(272, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)