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Properties

Label 144.12.u
Level $144$
Weight $12$
Character orbit 144.u
Rep. character $\chi_{144}(11,\cdot)$
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.u (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

\( 1048 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 30350 q^{6} - 4 q^{7} + O(q^{10}) \) \( 1048 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 30350 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 3663520 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} + 18646022 q^{18} - 8 q^{19} - 116040504 q^{20} + 354290 q^{21} - 2 q^{22} - 12 q^{23} + 233546592 q^{24} - 66817600 q^{27} + 16777208 q^{28} - 6 q^{29} + 361662566 q^{30} - 6 q^{32} - 8 q^{33} + 4094 q^{34} - 879714218 q^{36} - 8 q^{37} - 6 q^{38} + 579959968 q^{39} - 2 q^{40} + 962401428 q^{42} - 2 q^{43} + 97656246 q^{45} + 5480343536 q^{46} - 9950862006 q^{48} - 141237624504 q^{49} + 17550904716 q^{50} - 7186112796 q^{51} - 2 q^{52} + 11057749654 q^{54} - 16 q^{55} + 11863960452 q^{56} + 10743544924 q^{58} - 37356644922 q^{59} + 53953961254 q^{60} - 2 q^{61} + 11407705876 q^{64} - 12 q^{65} + 134001973772 q^{66} - 2 q^{67} + 49287335424 q^{68} - 354298 q^{69} - 3954653488 q^{70} - 123124841434 q^{72} + 66178276998 q^{74} - 114290252504 q^{75} - 45007939934 q^{76} - 6 q^{77} + 133983777432 q^{78} - 8 q^{81} + 104819662236 q^{82} + 17055758214 q^{83} + 420756379214 q^{84} + 97656248 q^{85} + 284043341934 q^{86} - 50128110096 q^{87} - 105633878570 q^{88} + 621369277216 q^{90} + 7909306964 q^{91} + 118594537092 q^{92} + 69689064734 q^{93} + 8190 q^{94} - 498493101946 q^{96} - 4 q^{97} + 252113728462 q^{99} + O(q^{100}) \)

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.