# Properties

 Label 64.24.a Level $64$ Weight $24$ Character orbit 64.a Rep. character $\chi_{64}(1,\cdot)$ Character field $\Q$ Dimension $45$ Newform subspaces $15$ Sturm bound $192$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$24$$ Character orbit: $$[\chi]$$ $$=$$ 64.a (trivial) Character field: $$\Q$$ Newform subspaces: $$15$$ Sturm bound: $$192$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{24}(\Gamma_0(64))$$.

Total New Old
Modular forms 190 47 143
Cusp forms 178 45 133
Eisenstein series 12 2 10

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$Dim.
$$+$$$$23$$
$$-$$$$22$$

## Trace form

 $$45q + 2q^{5} + 1349385563185q^{9} + O(q^{10})$$ $$45q + 2q^{5} + 1349385563185q^{9} + 14679969102058q^{13} - 112605054449254q^{17} - 2816606854453696q^{21} + 105092127635497067q^{25} + 40182344820854170q^{29} + 260763942015821088q^{33} - 3695983292865254398q^{37} - 423812055285736334q^{41} - 35506741043187658710q^{45} + 152483020894736533909q^{49} - 243471567206378773166q^{53} + 129888226131192780000q^{57} + 1404185762766222462618q^{61} - 752271782548128529884q^{65} - 1600174754769361596736q^{69} - 519127924113046457854q^{73} - 6333175115321920567104q^{77} + 50636703660686542572901q^{81} - 16258801490543646978172q^{85} - 6125289963067125364814q^{89} + 151248897441191345975552q^{93} + 66355999775620624191818q^{97} + O(q^{100})$$

## Decomposition of $$S_{24}^{\mathrm{new}}(\Gamma_0(64))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2
64.24.a.a $$1$$ $$214.531$$ $$\Q$$ None $$0$$ $$-505908$$ $$90135570$$ $$-6872255096$$ $$-$$ $$q-505908q^{3}+90135570q^{5}-6872255096q^{7}+\cdots$$
64.24.a.b $$1$$ $$214.531$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$206464378$$ $$0$$ $$-$$ $$q+206464378q^{5}-3^{23}q^{9}-7436301651582q^{13}+\cdots$$
64.24.a.c $$1$$ $$214.531$$ $$\Q$$ None $$0$$ $$505908$$ $$90135570$$ $$6872255096$$ $$+$$ $$q+505908q^{3}+90135570q^{5}+6872255096q^{7}+\cdots$$
64.24.a.d $$2$$ $$214.531$$ $$\Q(\sqrt{144169})$$ None $$0$$ $$-339480$$ $$-73069020$$ $$-1359184400$$ $$+$$ $$q+(-169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots$$
64.24.a.e $$2$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{2} - \cdots)$$ None $$0$$ $$-170520$$ $$92266020$$ $$192083440$$ $$+$$ $$q+(-85260-\beta )q^{3}+(46133010+540\beta )q^{5}+\cdots$$
64.24.a.f $$2$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{2} - \cdots)$$ None $$0$$ $$170520$$ $$92266020$$ $$-192083440$$ $$-$$ $$q+(85260-\beta )q^{3}+(46133010-540\beta )q^{5}+\cdots$$
64.24.a.g $$2$$ $$214.531$$ $$\Q(\sqrt{144169})$$ None $$0$$ $$339480$$ $$-73069020$$ $$1359184400$$ $$-$$ $$q+(169740-3\beta )q^{3}+(-36534510+\cdots)q^{5}+\cdots$$
64.24.a.h $$3$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$-213948$$ $$-95628618$$ $$8647912920$$ $$-$$ $$q+(-71316-\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots$$
64.24.a.i $$3$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$-32708$$ $$-31480650$$ $$993025320$$ $$+$$ $$q+(-10903-\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots$$
64.24.a.j $$3$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$32708$$ $$-31480650$$ $$-993025320$$ $$-$$ $$q+(10903+\beta _{1})q^{3}+(-10493544+\cdots)q^{5}+\cdots$$
64.24.a.k $$3$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$213948$$ $$-95628618$$ $$-8647912920$$ $$+$$ $$q+(71316+\beta _{1})q^{3}+(-31876206+\cdots)q^{5}+\cdots$$
64.24.a.l $$4$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$0$$ $$0$$ $$-19990040$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+(-4997510-5\beta _{2})q^{5}+\cdots$$
64.24.a.m $$6$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$-483920$$ $$6100380$$ $$-347289696$$ $$+$$ $$q+(-80653+\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots$$
64.24.a.n $$6$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$0$$ $$-163121700$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+(-27186950-\beta _{2})q^{5}+\cdots$$
64.24.a.o $$6$$ $$214.531$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$483920$$ $$6100380$$ $$347289696$$ $$+$$ $$q+(80653-\beta _{1})q^{3}+(1016775+135\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{24}^{\mathrm{old}}(\Gamma_0(64))$$ into lower level spaces

$$S_{24}^{\mathrm{old}}(\Gamma_0(64)) \cong$$ $$S_{24}^{\mathrm{new}}(\Gamma_0(1))$$$$^{\oplus 7}$$$$\oplus$$$$S_{24}^{\mathrm{new}}(\Gamma_0(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{24}^{\mathrm{new}}(\Gamma_0(4))$$$$^{\oplus 5}$$$$\oplus$$$$S_{24}^{\mathrm{new}}(\Gamma_0(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{24}^{\mathrm{new}}(\Gamma_0(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{24}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 2}$$