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Properties

Label 273.12.t
Level $273$
Weight $12$
Character orbit 273.t
Rep. character $\chi_{273}(4,\cdot)$
Character field $\Q(\zeta_{6})$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 410 q - 729 q^{3} - 417792 q^{4} + 102692 q^{7} - 12105045 q^{9} + O(q^{10}) \) \( 410 q - 729 q^{3} - 417792 q^{4} + 102692 q^{7} - 12105045 q^{9} + 800000 q^{10} - 1974732 q^{11} + 1990656 q^{12} - 630254 q^{13} + 1171536 q^{14} + 415202928 q^{16} - 9831176 q^{17} + 19135863 q^{19} + 89925000 q^{20} - 26156277 q^{21} - 17852110 q^{22} + 21199736 q^{23} + 2022470671 q^{25} - 359457706 q^{26} + 86093442 q^{27} - 489443894 q^{28} + 171868320 q^{29} + 105799653 q^{31} + 157537334 q^{35} + 12335099904 q^{36} - 2103696388 q^{38} + 1048849965 q^{39} - 1795644410 q^{40} + 669956382 q^{41} + 2863955718 q^{42} + 1475764132 q^{43} + 4369543368 q^{44} - 8883176508 q^{47} - 4586471424 q^{48} - 2318370390 q^{49} + 12195434694 q^{50} - 1055323728 q^{51} - 8762731380 q^{52} - 9768342376 q^{53} - 11996209986 q^{55} - 17936729598 q^{56} - 26525172516 q^{58} + 15467015124 q^{60} - 2843869429 q^{61} + 758887348 q^{62} - 4539982365 q^{63} - 406100460416 q^{64} - 49589966534 q^{65} - 20037321216 q^{66} + 14329013475 q^{67} + 110142481352 q^{68} + 32466645828 q^{69} - 131690090196 q^{70} - 25837929198 q^{71} + 32593719186 q^{73} + 34251175680 q^{74} - 129294944766 q^{75} - 58428604416 q^{76} - 20755081234 q^{77} + 34306467354 q^{78} + 55363013739 q^{79} - 184166400000 q^{80} - 714790802205 q^{81} + 173560946226 q^{82} + 107136110592 q^{84} + 121580191920 q^{85} - 201047262336 q^{86} + 251631714780 q^{87} - 21597813492 q^{88} - 94478400000 q^{90} + 267832836336 q^{91} - 73300078244 q^{92} - 306307196140 q^{94} + 83102104 q^{95} - 375000829470 q^{96} - 425672593851 q^{97} + 118608021042 q^{98} + O(q^{100}) \)

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

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