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Properties

Label 273.12.cd
Level $273$
Weight $12$
Character orbit 273.cd
Rep. character $\chi_{273}(44,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1624$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.cd (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 1656 1656 0
Cusp forms 1624 1624 0
Eisenstein series 32 32 0

Trace form

\( 1624 q - 4 q^{3} - 8200 q^{6} + 28190 q^{7} - 4 q^{9} + O(q^{10}) \) \( 1624 q - 4 q^{3} - 8200 q^{6} + 28190 q^{7} - 4 q^{9} - 16 q^{13} + 12491028 q^{15} + 813694968 q^{16} - 2598914 q^{18} - 45904542 q^{19} + 9534618 q^{21} - 32 q^{22} + 8751092 q^{24} - 186246184 q^{27} - 124019684 q^{28} - 603617822 q^{31} + 478024916 q^{33} - 1902277824 q^{34} + 46682150 q^{37} - 2226481328 q^{39} + 2580713488 q^{40} + 4191413888 q^{42} - 4391892122 q^{45} + 648375288 q^{46} - 21221211112 q^{48} - 7277580292 q^{52} - 6560661634 q^{54} + 6857449968 q^{55} + 3185420884 q^{57} + 17887271700 q^{58} - 19895364760 q^{60} - 5872607832 q^{61} - 22369099456 q^{63} - 43679239324 q^{66} + 27531128438 q^{67} + 24789632580 q^{70} - 34048015046 q^{72} - 53325841858 q^{73} + 326170255344 q^{76} - 69984310256 q^{78} - 135899380624 q^{79} + 191044513620 q^{81} + 138398198110 q^{84} + 273225822208 q^{85} + 108958412584 q^{87} - 54826457918 q^{91} - 78641720120 q^{93} + 567716400624 q^{94} - 420059631798 q^{96} - 36832460896 q^{97} + 166858396316 q^{99} + O(q^{100}) \)

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.