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Properties

Label 273.12.j
Level $273$
Weight $12$
Character orbit 273.j
Rep. character $\chi_{273}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $410$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(273, [\chi])\).

Total New Old
Modular forms 830 410 420
Cusp forms 814 410 404
Eisenstein series 16 0 16

Trace form

\( 410 q - 1458 q^{3} - 208896 q^{4} - 82739 q^{7} + 24210090 q^{9} + O(q^{10}) \) \( 410 q - 1458 q^{3} - 208896 q^{4} - 82739 q^{7} + 24210090 q^{9} - 1600000 q^{10} + 1316488 q^{11} + 1990656 q^{12} + 630254 q^{13} - 3903152 q^{14} - 216023240 q^{16} - 4915588 q^{17} + 38196014 q^{19} + 29975000 q^{20} - 3671487 q^{21} + 6137294 q^{22} + 10599868 q^{23} - 192846744 q^{24} - 2022470671 q^{25} - 106714042 q^{26} - 86093442 q^{27} + 429352166 q^{28} + 171868320 q^{29} + 40192669 q^{31} - 237456140 q^{32} - 1250735752 q^{34} - 126199834 q^{35} - 12335099904 q^{36} + 945997317 q^{37} - 1501545732 q^{38} - 874261512 q^{39} + 3119555590 q^{40} + 208983870 q^{41} - 81211086 q^{42} + 884559364 q^{43} - 2587736680 q^{44} - 3540389356 q^{46} - 2961058836 q^{47} + 4586471424 q^{48} + 116251549 q^{49} + 3964851266 q^{50} + 883479960 q^{51} - 12355555424 q^{52} + 4104570360 q^{53} + 20213990014 q^{55} + 7982027630 q^{56} + 4346531766 q^{57} - 6096895976 q^{58} + 16260251552 q^{59} - 11275371072 q^{60} - 33544250458 q^{61} + 2991586124 q^{62} - 4885655211 q^{63} + 393419233744 q^{64} + 47896783248 q^{65} + 20037321216 q^{66} + 29475445926 q^{67} + 24869868004 q^{68} + 17582357340 q^{69} + 85268337716 q^{70} - 64848325366 q^{71} + 52547064004 q^{73} - 17125587840 q^{74} + 35020496367 q^{75} - 46651715584 q^{76} + 208201188130 q^{77} + 62084838366 q^{78} - 68388454635 q^{79} + 38384213368 q^{80} + 1429581604410 q^{81} - 279066694732 q^{82} + 52602983168 q^{83} + 137979832320 q^{84} - 56074343740 q^{85} - 61551345488 q^{86} + 113426184546 q^{87} + 115171456488 q^{88} + 232059716624 q^{89} - 94478400000 q^{90} - 235357329903 q^{91} - 499481705972 q^{92} - 49961741139 q^{93} - 513192989648 q^{94} - 122763498948 q^{95} + 72474789366 q^{96} + 355261858569 q^{97} + 542748684538 q^{98} + 77737299912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{12}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)