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Properties

Label 273.12.y
Level $273$
Weight $12$
Character orbit 273.y
Rep. character $\chi_{273}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $814$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
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 830 830 0
Cusp forms 814 814 0
Eisenstein series 16 16 0

Trace form

\( 814 q - 413694 q^{4} + 25801 q^{7} - 64158 q^{9} + O(q^{10}) \) \( 814 q - 413694 q^{4} + 25801 q^{7} - 64158 q^{9} - 6150 q^{12} + 3859670 q^{13} - 1337697 q^{15} - 417329150 q^{16} + 3898368 q^{18} - 10519766 q^{19} + 531441 q^{21} + 11986506 q^{22} - 1062888 q^{24} + 3837890621 q^{25} + 157186042 q^{28} + 16099856 q^{30} - 715966981 q^{31} - 758975214 q^{33} + 24576 q^{34} + 491694236 q^{36} + 1726557771 q^{37} - 2069358783 q^{39} - 2571816570 q^{40} - 1329921672 q^{42} + 2130642796 q^{43} - 3 q^{45} - 972538368 q^{46} + 13658082 q^{48} - 4766018151 q^{49} + 8371602466 q^{51} - 2488879456 q^{52} - 9841004739 q^{54} - 5436056250 q^{55} + 4402854927 q^{60} + 27151587639 q^{63} + 830765407344 q^{64} - 13209989139 q^{66} + 19936226505 q^{69} + 61205363124 q^{70} - 46632522046 q^{73} + 61268240916 q^{75} + 21544468480 q^{76} + 162654410131 q^{78} - 97156676529 q^{79} - 81242336694 q^{81} - 193636822794 q^{84} + 190713866922 q^{85} - 141447887853 q^{87} - 211770308076 q^{88} + 41410297921 q^{91} + 282281546955 q^{93} + 1088397312 q^{96} - 46408945961 q^{97} + O(q^{100}) \)

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.