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Properties

Label 273.12.cg
Level $273$
Weight $12$
Character orbit 273.cg
Rep. character $\chi_{273}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $820$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 820 840
Cusp forms 1628 820 808
Eisenstein series 32 0 32

Trace form

\( 820 q - 56932 q^{7} - 48420180 q^{9} + O(q^{10}) \) \( 820 q - 56932 q^{7} - 48420180 q^{9} + 1316488 q^{11} + 1990656 q^{12} - 6076320 q^{14} + 423624704 q^{16} - 49488290 q^{19} + 22484790 q^{21} - 11714816 q^{22} + 337392060 q^{26} + 451595688 q^{28} + 135094256 q^{29} + 152541832 q^{31} - 237456140 q^{32} - 125350000 q^{35} - 127010304 q^{37} + 1748523024 q^{39} + 3971733540 q^{40} + 43004772 q^{41} + 2421102312 q^{42} - 890774772 q^{43} - 9219724496 q^{44} + 2539991116 q^{46} - 5555679346 q^{49} + 15959698696 q^{50} - 515531304 q^{51} + 25834323932 q^{52} + 5663772016 q^{53} + 24653340084 q^{55} + 98661768300 q^{56} + 4346531766 q^{57} + 18091078680 q^{58} + 6119699364 q^{60} - 11251420416 q^{62} + 3361777668 q^{63} + 7335125128 q^{65} - 13499548214 q^{67} + 90604118016 q^{68} - 76782605464 q^{70} + 3330450468 q^{71} - 171598636474 q^{73} + 115479552256 q^{74} - 33222656250 q^{75} + 167704367104 q^{76} + 96391305720 q^{78} - 13025440896 q^{79} - 368332800000 q^{80} + 2859163208820 q^{81} - 124924259328 q^{82} - 67180186704 q^{83} + 244749164544 q^{84} - 43417327156 q^{85} + 509379558096 q^{86} + 37169018532 q^{87} - 224034180528 q^{89} - 208120464670 q^{91} - 572781784216 q^{92} + 115175631942 q^{93} + 368415150000 q^{95} - 157576461372 q^{96} + 251575406978 q^{97} - 152002170072 q^{98} - 77737299912 q^{99} + O(q^{100}) \)

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

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