# Properties

 Label 72.7.p Level $72$ Weight $7$ Character orbit 72.p Rep. character $\chi_{72}(43,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $140$ Newform subspaces $2$ Sturm bound $84$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 72.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$84$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(72, [\chi])$$.

Total New Old
Modular forms 148 148 0
Cusp forms 140 140 0
Eisenstein series 8 8 0

## Trace form

 $$140 q - q^{2} - 4 q^{3} - q^{4} - 193 q^{6} - 274 q^{8} - 4 q^{9} + O(q^{10})$$ $$140 q - q^{2} - 4 q^{3} - q^{4} - 193 q^{6} - 274 q^{8} - 4 q^{9} - 132 q^{10} - 2 q^{11} + 3092 q^{12} + 2346 q^{14} - q^{16} - 8 q^{17} - 4222 q^{18} - 8 q^{19} + 3588 q^{20} + 127 q^{22} - 27001 q^{24} + 193748 q^{25} + 38352 q^{26} - 34324 q^{27} - 8196 q^{28} - 107130 q^{30} - 126181 q^{32} - 42626 q^{33} + 19933 q^{34} - 62508 q^{35} + 45227 q^{36} + 270079 q^{38} - 27126 q^{40} - 10442 q^{41} - 107478 q^{42} - 2 q^{43} - 819398 q^{44} + 22296 q^{46} + 502487 q^{48} + 974804 q^{49} - 594727 q^{50} + 380680 q^{51} + 62952 q^{52} + 834797 q^{54} - 587718 q^{56} + 119200 q^{57} + 221136 q^{58} + 403918 q^{59} - 960810 q^{60} - 1062312 q^{62} + 263930 q^{64} - 62502 q^{65} - 57518 q^{66} - 2 q^{67} + 571489 q^{68} + 86334 q^{70} - 1909105 q^{72} - 8 q^{73} - 782586 q^{74} + 2732348 q^{75} - 432083 q^{76} - 3340578 q^{78} + 2446320 q^{80} + 8228 q^{81} - 965126 q^{82} - 1537202 q^{83} - 227136 q^{84} + 1516429 q^{86} + 12427 q^{88} - 1175336 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 5425010 q^{96} - 2 q^{97} + 2767082 q^{98} + 4048222 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.7.p.a $4$ $16.564$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$16$$ $$-46$$ $$0$$ $$0$$ $$q+8\beta _{2}q^{2}+(-\beta _{1}-23\beta _{2}+\beta _{3})q^{3}+\cdots$$
72.7.p.b $136$ $16.564$ None $$-17$$ $$42$$ $$0$$ $$0$$