Properties

Label 273.12.bw
Level $273$
Weight $12$
Character orbit 273.bw
Rep. character $\chi_{273}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1628$
Sturm bound $448$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1660 1660 0
Cusp forms 1628 1628 0
Eisenstein series 32 32 0

Trace form

\( 1628 q - 4 q^{3} - 12 q^{4} + 4088 q^{6} - 90992 q^{7} - 4 q^{9} + O(q^{10}) \) \( 1628 q - 4 q^{3} - 12 q^{4} + 4088 q^{6} - 90992 q^{7} - 4 q^{9} - 2125764 q^{12} - 16 q^{13} - 6245526 q^{15} + 834666500 q^{16} + 37823230 q^{18} + 2773370 q^{19} + 8471736 q^{21} - 8 q^{22} - 16414732 q^{24} - 186246184 q^{27} - 86406116 q^{28} - 239476684 q^{31} - 197074630 q^{33} + 951138888 q^{34} - 788348940 q^{36} - 2203374288 q^{37} + 1901004544 q^{39} - 1290356756 q^{40} - 614332660 q^{42} + 4408646148 q^{43} - 3805954622 q^{45} + 5762592504 q^{46} + 10585439720 q^{48} + 5555679334 q^{49} + 2125764 q^{51} + 10062217212 q^{52} + 13121335550 q^{54} - 3428725008 q^{55} - 1592710454 q^{57} - 253733868 q^{58} - 19920555160 q^{60} + 11745215640 q^{61} - 12050779324 q^{63} + 5465564486 q^{66} + 25731220498 q^{67} - 67205445354 q^{69} - 45260576424 q^{70} + 95709230470 q^{72} - 37502289158 q^{73} - 2125770 q^{75} + 158516219888 q^{76} - 232724099342 q^{78} + 44812520168 q^{79} + 17001236868 q^{81} - 319441670408 q^{84} + 140327767504 q^{85} - 173935237346 q^{87} + 288840579730 q^{91} - 75829195628 q^{93} + 567716400624 q^{94} - 417880723698 q^{96} + 545385053730 q^{97} - 83429198170 q^{99} + O(q^{100}) \)

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

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