Properties

Label 72.22.l
Level $72$
Weight $22$
Character orbit 72.l
Rep. character $\chi_{72}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $500$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(72, [\chi])\).

Total New Old
Modular forms 508 508 0
Cusp forms 500 500 0
Eisenstein series 8 8 0

Trace form

\( 500 q - 3 q^{2} - 4 q^{3} - q^{4} + 69283301 q^{6} - 4 q^{9} + O(q^{10}) \) \( 500 q - 3 q^{2} - 4 q^{3} - q^{4} + 69283301 q^{6} - 4 q^{9} + 4194300 q^{10} - 6 q^{11} + 138859525310 q^{12} + 3424745318472 q^{14} - q^{16} + 56200584070826 q^{18} - 8 q^{19} + 141949831039398 q^{20} - 4194305 q^{22} - 636099929707771 q^{24} - 23078918457031252 q^{25} + 1147739795850512 q^{27} - 8796093022212 q^{28} - 8855945703211044 q^{30} + 27944572626756027 q^{32} - 10718205122066114 q^{33} + 2860283542229125 q^{34} + 74718907106134295 q^{36} + 84359019735514551 q^{38} + 42588324033203124 q^{40} + 125026581602455614 q^{41} - 21146004866398032 q^{42} - 2 q^{43} + 226626385818303552 q^{46} + 132857598459299021 q^{48} + 18990559378831656236 q^{49} - 862419361556898939 q^{50} + 2352404156896142908 q^{51} - 147761071869131742 q^{52} - 2541731429271173101 q^{54} + 4263080368535548494 q^{56} + 1689283451112476188 q^{57} + 3029449227257522094 q^{58} + 29462177304886525374 q^{59} + 14240572204015344252 q^{60} - 4366766790372691966 q^{64} - 6 q^{65} + 37495635927222336490 q^{66} - 2 q^{67} + 32885424744651089631 q^{68} + 559499538401787408 q^{70} + 72537676096966400243 q^{72} - 8 q^{73} + 384945318480465601572 q^{74} + 58515596943132330308 q^{75} - 22082012104852762031 q^{76} - 63342976352669674932 q^{78} + 8713144516687115384 q^{81} + 129661334538993235978 q^{82} - 1013832965086622050986 q^{83} + 1153486581232573890780 q^{84} + 494763142547393599233 q^{86} - 136639359549165561005 q^{88} - 479605588537110694914 q^{90} - 2234183456333136036 q^{91} - 385885262925919772376 q^{92} - 165302765209868718810 q^{94} + 5391081991931549791418 q^{96} - 2 q^{97} - 1536422979428726832950 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

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