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Properties

Label 273.12.k
Level $273$
Weight $12$
Character orbit 273.k
Rep. character $\chi_{273}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $312$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 828 312 516
Cusp forms 812 312 500
Eisenstein series 16 0 16

Trace form

\( 312 q + 128 q^{2} - 163840 q^{4} - 41728 q^{5} - 786432 q^{8} - 9211644 q^{9} + O(q^{10}) \) \( 312 q + 128 q^{2} - 163840 q^{4} - 41728 q^{5} - 786432 q^{8} - 9211644 q^{9} + 192248 q^{10} - 61076 q^{11} + 937008 q^{12} - 29932 q^{13} - 1091556 q^{15} - 180616376 q^{16} - 19002004 q^{17} - 15116544 q^{18} - 21920792 q^{19} + 15924232 q^{20} - 78543620 q^{22} - 80378152 q^{23} + 2998637624 q^{25} + 632109800 q^{26} + 123205908 q^{29} - 64896552 q^{30} + 1508451320 q^{31} + 1739715096 q^{32} - 223891452 q^{33} - 483510824 q^{34} - 202557964 q^{35} - 9674588160 q^{36} - 920895616 q^{37} + 267278392 q^{38} - 590153688 q^{39} + 5387147096 q^{40} - 2391536984 q^{41} - 522764928 q^{42} + 270354332 q^{43} + 15810099312 q^{44} + 1231998336 q^{45} - 3783442976 q^{46} - 10378583664 q^{47} - 4040421264 q^{48} - 44066138844 q^{49} - 7404394220 q^{50} + 10868964264 q^{51} - 12055378396 q^{52} + 4299515264 q^{53} - 28948530348 q^{55} + 1567495580 q^{58} - 3629309244 q^{59} + 19253370168 q^{60} - 15139018992 q^{61} - 12378971708 q^{62} + 413490281896 q^{64} + 43681862060 q^{65} + 29672146800 q^{66} - 7927622836 q^{67} - 2001298952 q^{68} + 14330529396 q^{69} + 3132555888 q^{70} + 24353563104 q^{71} + 23219011584 q^{72} + 190199979968 q^{73} + 183638907424 q^{74} + 28206440784 q^{75} + 61105836968 q^{76} + 9353028272 q^{77} - 30512790720 q^{78} + 320282171416 q^{79} - 60225258784 q^{80} - 543938366556 q^{81} - 258137023756 q^{82} + 97980600368 q^{83} + 66155216668 q^{85} + 78246662848 q^{86} + 55105621272 q^{87} - 230200833612 q^{88} - 321128098176 q^{89} - 22704104304 q^{90} - 68724091912 q^{91} + 462293261912 q^{92} + 177007434936 q^{94} + 137519099740 q^{95} - 187710666840 q^{96} - 763891407700 q^{97} + 36156831872 q^{98} + 7212953448 q^{99} + O(q^{100}) \)

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

\( S_{12}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)