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Properties

Label 272.10.v
Level $272$
Weight $10$
Character orbit 272.v
Rep. character $\chi_{272}(49,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $320$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
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 1320 328 992
Cusp forms 1272 320 952
Eisenstein series 48 8 40

Trace form

\( 320 q + 4 q^{3} - 4 q^{5} + 4 q^{7} + 55476 q^{9} + O(q^{10}) \) \( 320 q + 4 q^{3} - 4 q^{5} + 4 q^{7} + 55476 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} + 961780 q^{19} + 4 q^{23} + 1721760 q^{25} + 4 q^{27} + 2126872 q^{29} + 4 q^{31} - 8 q^{33} + 72030008 q^{35} - 4 q^{37} - 78728 q^{39} - 3780960 q^{41} + 4 q^{43} + 47107976 q^{45} - 4 q^{49} + 234714204 q^{51} + 68323680 q^{53} - 39989396 q^{57} - 73420436 q^{59} - 40134996 q^{61} + 774238000 q^{63} - 149202724 q^{65} - 613292128 q^{67} + 340439832 q^{69} + 585305036 q^{71} + 604274376 q^{73} + 979758652 q^{75} + 463520652 q^{77} - 1173770516 q^{79} - 156606780 q^{83} + 887587680 q^{85} - 1543297460 q^{87} - 161414424 q^{91} + 2410246364 q^{93} + 4 q^{95} - 196950748 q^{97} - 4069082432 q^{99} + O(q^{100}) \)

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

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