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Properties

Label 273.12.bj
Level $273$
Weight $12$
Character orbit 273.bj
Rep. character $\chi_{273}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $412$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.bj (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 828 412 416
Cusp forms 812 412 400
Eisenstein series 16 0 16

Trace form

\( 412 q - 486 q^{3} + 212992 q^{4} - 12164094 q^{9} + O(q^{10}) \) \( 412 q - 486 q^{3} + 212992 q^{4} - 12164094 q^{9} + 800000 q^{10} + 995328 q^{12} + 1819922 q^{13} - 8949024 q^{14} - 230719888 q^{16} + 4915588 q^{17} - 36263992 q^{22} - 10599868 q^{23} + 2090830046 q^{25} - 5749978 q^{26} + 57395628 q^{27} - 343736640 q^{29} + 818174336 q^{35} - 25153929216 q^{36} + 3304166792 q^{38} - 109282689 q^{39} - 3781511180 q^{40} + 1048128984 q^{42} - 697745212 q^{43} + 4076863488 q^{48} + 519895958 q^{49} - 797558076 q^{51} - 4062848224 q^{52} + 11041026728 q^{53} + 38359585056 q^{55} - 47632289904 q^{56} - 38071862468 q^{61} + 86393318608 q^{62} - 581414238088 q^{64} - 9612463658 q^{65} - 20037321216 q^{66} - 55071240676 q^{68} - 64933291656 q^{69} + 34251175680 q^{74} + 3595680234 q^{75} + 133882308476 q^{77} - 35179804980 q^{78} - 14021446234 q^{79} - 718277586606 q^{81} + 91288483104 q^{82} - 107231348124 q^{87} + 97177499112 q^{88} - 94478400000 q^{90} - 140104244497 q^{91} + 525370242112 q^{92} - 297333393832 q^{94} + 129207386740 q^{95} + O(q^{100}) \)

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

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