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Properties

Label 272.10.l
Level $272$
Weight $10$
Character orbit 272.l
Rep. character $\chi_{272}(69,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 652 576 76
Cusp forms 644 576 68
Eisenstein series 8 0 8

Trace form

\( 576 q - 340 q^{4} + 4380 q^{6} + 1428 q^{8} + O(q^{10}) \) \( 576 q - 340 q^{4} + 4380 q^{6} + 1428 q^{8} + 35628 q^{10} - 131720 q^{11} - 434316 q^{12} + 48020 q^{14} + 566100 q^{16} - 2230740 q^{18} + 4745972 q^{20} + 3305788 q^{22} - 6464288 q^{24} + 12695532 q^{26} - 12650088 q^{27} + 1266800 q^{29} - 1712264 q^{30} + 22164504 q^{31} - 25660820 q^{32} - 38240616 q^{35} - 54356320 q^{36} + 2429552 q^{37} + 40137748 q^{38} - 29204020 q^{40} - 58208000 q^{42} + 69762152 q^{43} - 5416080 q^{44} - 13265320 q^{48} - 3320525376 q^{49} + 127557732 q^{50} + 293147388 q^{52} + 149815696 q^{53} - 493427364 q^{54} + 335891492 q^{56} - 3807504 q^{58} + 99068520 q^{59} - 208771584 q^{60} - 25230956 q^{62} + 630118440 q^{63} + 357383396 q^{64} - 1471440656 q^{66} - 812335344 q^{67} - 1775777976 q^{70} + 1443734928 q^{72} + 1091091652 q^{74} + 2069860456 q^{75} + 1824931028 q^{76} - 412088432 q^{77} + 3266644024 q^{78} - 1558003240 q^{79} - 1684602388 q^{80} - 24794911296 q^{81} + 1214703972 q^{82} + 795523160 q^{83} - 2181878600 q^{84} - 2244459452 q^{86} - 3866240844 q^{88} - 4212087624 q^{90} + 6880895336 q^{92} - 2143933104 q^{93} + 1015829152 q^{94} + 10174826512 q^{95} + 2609675480 q^{96} + 4424652696 q^{98} - 5877899624 q^{99} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(272, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)