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Properties

Label 273.12.n
Level $273$
Weight $12$
Character orbit 273.n
Rep. character $\chi_{273}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $616$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 832 616 216
Cusp forms 816 616 200
Eisenstein series 16 0 16

Trace form

\( 616 q + 60708 q^{6} + O(q^{10}) \) \( 616 q + 60708 q^{6} - 6896936 q^{13} - 6599812 q^{15} - 654834032 q^{16} - 1903508 q^{18} - 21920792 q^{19} + 25076044 q^{21} + 122299952 q^{22} + 234855136 q^{24} + 169104648 q^{27} - 188013776 q^{31} + 595081116 q^{33} + 1056427008 q^{34} - 821234256 q^{37} - 3147031208 q^{39} + 2463230192 q^{40} - 8138362124 q^{45} - 391362144 q^{46} + 15005761536 q^{48} + 19827059544 q^{52} + 37009226652 q^{54} - 14009039712 q^{55} - 18237138560 q^{57} + 47252230320 q^{58} - 40328043196 q^{60} + 22193740896 q^{61} - 13018164376 q^{63} + 110225982632 q^{66} - 46898297752 q^{67} - 1566277944 q^{70} + 68121531440 q^{72} - 68086271632 q^{73} - 207091400984 q^{76} - 146998345532 q^{78} - 272738032160 q^{79} + 89887281992 q^{81} - 53109246036 q^{84} - 85167606304 q^{85} + 156393212496 q^{87} + 68724091912 q^{91} + 347109887524 q^{93} + 814854336336 q^{94} - 101105257096 q^{96} + 166142684256 q^{97} - 831656210364 q^{99} + O(q^{100}) \)

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

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