Properties

Label 72.22.i
Level $72$
Weight $22$
Character orbit 72.i
Rep. character $\chi_{72}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $126$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 72.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 512 126 386
Cusp forms 496 126 370
Eisenstein series 16 0 16

Trace form

\( 126 q + 67717 q^{3} + 19531250 q^{5} - 15969907213 q^{9} + O(q^{10}) \) \( 126 q + 67717 q^{3} + 19531250 q^{5} - 15969907213 q^{9} - 166158643531 q^{11} - 4903488160334 q^{15} - 13190094470534 q^{17} + 5596938571230 q^{19} + 92041381916796 q^{21} + 11720923501196 q^{23} - 6008148193359375 q^{25} + 3525471492838720 q^{27} + 5525953142740932 q^{29} - 725516191935270 q^{31} - 2792696191889591 q^{33} + 72793570896138132 q^{35} + 169701289300782778 q^{39} + 4249277668724661 q^{41} - 138074506063048629 q^{43} + 384635196894589610 q^{45} - 253388593232067816 q^{47} - 5516691290090627589 q^{49} - 1423073001195993775 q^{51} + 107249077848656576 q^{53} + 2929366543189254948 q^{55} + 9751892185194047567 q^{57} - 7095598541462230165 q^{59} - 1452504710346449526 q^{61} - 21734655685384396146 q^{63} + 4002038035389245726 q^{65} + 9513639154044746289 q^{67} - 22691808718452795818 q^{69} + 77822788192190357176 q^{71} + 60660995891184169254 q^{73} - 58423477030438947151 q^{75} + 185541128742101720988 q^{77} + 68699627718954256206 q^{79} + 490370656378363181207 q^{81} - 424212862356521187338 q^{83} - 29053786948405013268 q^{85} + 694851801786018187008 q^{87} - 1114589318272810804236 q^{89} - 388217133071228979540 q^{91} - 550135695050265243418 q^{93} + 822740048248730495896 q^{95} - 632660833151577860247 q^{97} - 5193711851625686983420 q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{22}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)