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Properties

Label 144.12.x
Level $144$
Weight $12$
Character orbit 144.x
Rep. character $\chi_{144}(13,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1048$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(144, [\chi])\).

Total New Old
Modular forms 1064 1064 0
Cusp forms 1048 1048 0
Eisenstein series 16 16 0

Trace form

\( 1048 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 30358 q^{6} - 8 q^{8} + O(q^{10}) \) \( 1048 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 30358 q^{6} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 3663512 q^{12} - 2 q^{13} - 8194 q^{14} - 8 q^{15} - 2 q^{16} - 16 q^{17} + 18637830 q^{18} - 8 q^{19} + 38680164 q^{20} - 354298 q^{21} - 2 q^{22} - 123021448 q^{24} - 393750760 q^{26} + 66817592 q^{27} - 16777224 q^{28} - 2 q^{29} - 161140194 q^{30} - 4 q^{31} - 851816662 q^{32} - 8 q^{33} - 4098 q^{34} - 195312508 q^{35} - 919996258 q^{36} - 8 q^{37} + 2959647122 q^{38} - 2 q^{40} + 1012764284 q^{42} - 2 q^{43} + 6008579316 q^{44} - 97656254 q^{45} - 5480359936 q^{46} + 9173800276 q^{47} + 643674914 q^{48} + 141237624496 q^{49} - 5850309768 q^{50} - 7187529972 q^{51} - 2 q^{52} - 8 q^{53} - 26691767578 q^{54} - 14980984556 q^{56} - 10743544928 q^{58} + 12452214970 q^{59} + 13021963470 q^{60} - 2 q^{61} - 99524566076 q^{62} - 7909306980 q^{63} + 11407705876 q^{64} - 4 q^{65} + 16922362100 q^{66} - 2 q^{67} + 16412334592 q^{68} - 354298 q^{69} + 3954653484 q^{70} - 49884802878 q^{72} + 22059425666 q^{74} + 114484856408 q^{75} + 45007939930 q^{76} - 7909306974 q^{77} - 44493725540 q^{78} - 4 q^{79} - 392102802288 q^{80} - 8 q^{81} + 104819645852 q^{82} - 5685252742 q^{83} - 244417602310 q^{84} - 97656252 q^{85} - 117469637354 q^{86} + 105633878566 q^{88} + 60893274648 q^{90} - 7909306980 q^{91} - 39548289584 q^{92} + 69689773322 q^{93} + 8190 q^{94} - 495219800004 q^{95} + 28584833590 q^{96} - 4 q^{97} + 55656554968 q^{98} + 126589490026 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

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