Properties

 Label 799.2.a Level $799$ Weight $2$ Character orbit 799.a Rep. character $\chi_{799}(1,\cdot)$ Character field $\Q$ Dimension $61$ Newform subspaces $7$ Sturm bound $144$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$799 = 17 \cdot 47$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 799.a (trivial) Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(799))$$.

Total New Old
Modular forms 74 61 13
Cusp forms 71 61 10
Eisenstein series 3 0 3

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

$$17$$$$47$$FrickeDim
$$+$$$$+$$$+$$$12$$
$$+$$$$-$$$-$$$20$$
$$-$$$$+$$$-$$$18$$
$$-$$$$-$$$+$$$11$$
Plus space$$+$$$$23$$
Minus space$$-$$$$38$$

Trace form

 $$61 q - q^{2} + 59 q^{4} + 6 q^{5} + 8 q^{6} - 16 q^{7} + 3 q^{8} + 69 q^{9} + O(q^{10})$$ $$61 q - q^{2} + 59 q^{4} + 6 q^{5} + 8 q^{6} - 16 q^{7} + 3 q^{8} + 69 q^{9} + 10 q^{10} + 4 q^{11} + 16 q^{12} - 10 q^{13} + 12 q^{14} - 4 q^{15} + 51 q^{16} - 3 q^{17} - 33 q^{18} - 4 q^{19} - 6 q^{20} - 16 q^{22} - 12 q^{24} + 55 q^{25} - 18 q^{26} + 24 q^{27} - 36 q^{28} + 14 q^{29} - 24 q^{30} - 8 q^{31} - 5 q^{32} - 8 q^{33} - q^{34} + 20 q^{35} + 19 q^{36} - 10 q^{37} - 24 q^{38} - 4 q^{39} + 6 q^{40} + 34 q^{41} - 20 q^{42} - 8 q^{43} + 4 q^{44} + 58 q^{45} - 24 q^{46} + q^{47} + 28 q^{48} + 41 q^{49} + q^{50} - 4 q^{51} - 14 q^{52} + 2 q^{53} + 16 q^{54} + 12 q^{55} - 36 q^{56} - 8 q^{57} + 34 q^{58} + 48 q^{59} - 64 q^{60} + 6 q^{61} + 44 q^{62} - 28 q^{63} + 75 q^{64} - 8 q^{65} - 24 q^{66} - 28 q^{67} - 5 q^{68} + 28 q^{69} + 32 q^{70} + 20 q^{71} - 13 q^{72} - 26 q^{73} - 54 q^{74} - 52 q^{75} - 8 q^{76} - 12 q^{77} + 32 q^{78} - 76 q^{79} + 58 q^{80} + 45 q^{81} + 46 q^{82} - 16 q^{83} + 2 q^{85} - 52 q^{86} - 20 q^{87} - 24 q^{88} + 46 q^{89} + 30 q^{90} - 4 q^{91} + 8 q^{92} + 12 q^{93} + 3 q^{94} - 44 q^{95} - 136 q^{96} - 62 q^{97} + 107 q^{98} - 40 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(799))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17 47
799.2.a.a $1$ $6.380$ $$\Q$$ None $$-1$$ $$2$$ $$0$$ $$-2$$ $-$ $-$ $$q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots$$
799.2.a.b $1$ $6.380$ $$\Q$$ None $$-1$$ $$2$$ $$4$$ $$-2$$ $-$ $+$ $$q-q^{2}+2q^{3}-q^{4}+4q^{5}-2q^{6}-2q^{7}+\cdots$$
799.2.a.c $2$ $6.380$ $$\Q(\sqrt{5})$$ None $$-3$$ $$0$$ $$-1$$ $$-2$$ $-$ $-$ $$q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots$$
799.2.a.d $8$ $6.380$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$1$$ $$-7$$ $$-10$$ $$-9$$ $-$ $-$ $$q-\beta _{6}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{7})q^{4}+\cdots$$
799.2.a.e $12$ $6.380$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-4$$ $$-1$$ $$-11$$ $$1$$ $+$ $+$ $$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
799.2.a.f $17$ $6.380$ $$\mathbb{Q}[x]/(x^{17} - \cdots)$$ None $$3$$ $$1$$ $$11$$ $$1$$ $-$ $+$ $$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots$$
799.2.a.g $20$ $6.380$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$4$$ $$3$$ $$13$$ $$-3$$ $+$ $-$ $$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{17}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(799))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(799)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(17))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(47))$$$$^{\oplus 2}$$