# Properties

 Label 72.22.d Level $72$ Weight $22$ Character orbit 72.d Rep. character $\chi_{72}(37,\cdot)$ Character field $\Q$ Dimension $104$ Sturm bound $264$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$22$$ Character orbit: $$[\chi]$$ $$=$$ 72.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Sturm bound: $$264$$

## Dimensions

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

Total New Old
Modular forms 256 106 150
Cusp forms 248 104 144
Eisenstein series 8 2 6

## Trace form

 $$104 q + 288 q^{2} - 2014208 q^{4} + 564950496 q^{7} - 1492285644 q^{8} + O(q^{10})$$ $$104 q + 288 q^{2} - 2014208 q^{4} + 564950496 q^{7} - 1492285644 q^{8} + 90709717084 q^{10} + 358858635492 q^{14} - 4044890602224 q^{16} + 1740714497004 q^{17} + 6837193514712 q^{20} + 131819252218604 q^{22} - 161368512043560 q^{23} - 9675978849059504 q^{25} + 951505374003216 q^{26} - 3474942103991944 q^{28} - 846275622597776 q^{31} - 11164133540125992 q^{32} - 14912496451861480 q^{34} - 110184531546778308 q^{38} + 212609964169191480 q^{40} - 1275406391815260 q^{41} + 611514238184919480 q^{44} + 307040096002655288 q^{46} + 1201891630581881304 q^{47} + 8459044424097555576 q^{49} - 1433176081008714936 q^{50} + 2725269242224911680 q^{52} + 5990869811401331584 q^{55} + 5539292337299731080 q^{56} + 1475215398509637500 q^{58} + 28482230208248799084 q^{62} - 34130272675038886352 q^{64} + 6300950222080771824 q^{65} - 81919510141327820328 q^{68} - 122834062654977310728 q^{70} + 5304472257548573832 q^{71} + 50320019149706706200 q^{73} - 113259105019947643752 q^{74} + 53841840072350156824 q^{76} - 141638797118125948224 q^{79} + 218385211396540716864 q^{80} - 136992077118582500624 q^{82} + 473594097775266739356 q^{86} - 740066823849593193424 q^{88} + 475852595948234668380 q^{89} - 1288323228520299761376 q^{92} - 1547475882369316075992 q^{94} - 417769040115929987280 q^{95} + 425373226204154892072 q^{97} - 1509026760744737377128 q^{98} + O(q^{100})$$

## 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

$$S_{22}^{\mathrm{old}}(72, [\chi]) \cong$$ $$S_{22}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$