# Properties

 Label 841.2.a Level $841$ Weight $2$ Character orbit 841.a Rep. character $\chi_{841}(1,\cdot)$ Character field $\Q$ Dimension $54$ Newform subspaces $11$ Sturm bound $145$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$841 = 29^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 841.a (trivial) Character field: $$\Q$$ Newform subspaces: $$11$$ Sturm bound: $$145$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(841))$$.

Total New Old
Modular forms 87 81 6
Cusp forms 58 54 4
Eisenstein series 29 27 2

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

$$29$$Dim
$$+$$$$24$$
$$-$$$$30$$

## Trace form

 $$54 q + 2 q^{2} - 2 q^{3} + 40 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} + 28 q^{9} + O(q^{10})$$ $$54 q + 2 q^{2} - 2 q^{3} + 40 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} + 28 q^{9} - 2 q^{10} - 2 q^{11} - 10 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} + 4 q^{22} + 4 q^{23} + 16 q^{24} + 8 q^{25} - 10 q^{26} - 2 q^{27} + 22 q^{28} - 28 q^{30} - 6 q^{31} - 6 q^{32} + 8 q^{33} + 10 q^{34} - 30 q^{36} + 8 q^{37} + 18 q^{38} + 10 q^{39} - 6 q^{40} - 8 q^{41} - 10 q^{42} - 10 q^{43} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 2 q^{47} - 6 q^{48} - 30 q^{49} - 8 q^{50} + 24 q^{52} + 2 q^{53} + 4 q^{54} + 2 q^{55} - 8 q^{56} - 8 q^{57} - 30 q^{59} + 10 q^{60} + 4 q^{61} - 28 q^{62} + 20 q^{63} - 22 q^{64} + 4 q^{65} - 2 q^{66} + 2 q^{67} - 12 q^{68} - 12 q^{69} + 8 q^{70} + 16 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 8 q^{75} - 12 q^{76} - 8 q^{77} - 10 q^{78} + 2 q^{79} + 16 q^{80} - 50 q^{81} - 6 q^{82} - 2 q^{83} + 24 q^{84} - 4 q^{85} + 16 q^{86} - 14 q^{88} + 8 q^{89} - 8 q^{90} - 4 q^{91} - 18 q^{92} - 16 q^{93} - 2 q^{94} + 12 q^{95} - 74 q^{96} + 8 q^{97} + 2 q^{98} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(841))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
841.2.a.a $2$ $6.715$ $$\Q(\sqrt{5})$$ None $$-1$$ $$1$$ $$1$$ $$0$$ $+$ $$q-\beta q^{2}+\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots$$
841.2.a.b $2$ $6.715$ $$\Q(\sqrt{5})$$ None $$0$$ $$0$$ $$6$$ $$4$$ $-$ $$q-\beta q^{2}+\beta q^{3}+3q^{4}+3q^{5}-5q^{6}+\cdots$$
841.2.a.c $2$ $6.715$ $$\Q(\sqrt{5})$$ None $$1$$ $$-1$$ $$1$$ $$0$$ $-$ $$q+\beta q^{2}-\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots$$
841.2.a.d $2$ $6.715$ $$\Q(\sqrt{2})$$ None $$2$$ $$-2$$ $$-2$$ $$0$$ $+$ $$q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots$$
841.2.a.e $3$ $6.715$ $$\Q(\zeta_{14})^+$$ None $$-1$$ $$1$$ $$-3$$ $$-3$$ $+$ $$q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
841.2.a.f $3$ $6.715$ $$\Q(\zeta_{14})^+$$ None $$1$$ $$-1$$ $$-3$$ $$-3$$ $+$ $$q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
841.2.a.g $6$ $6.715$ 6.6.11973625.1 None $$-2$$ $$-2$$ $$-2$$ $$-4$$ $+$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$$
841.2.a.h $6$ $6.715$ 6.6.11973625.1 None $$2$$ $$2$$ $$-2$$ $$-4$$ $-$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$$
841.2.a.i $8$ $6.715$ 8.8.2841328125.1 None $$-4$$ $$-6$$ $$-1$$ $$0$$ $+$ $$q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
841.2.a.j $8$ $6.715$ 8.8.2841328125.1 None $$4$$ $$6$$ $$-1$$ $$0$$ $-$ $$q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$$
841.2.a.k $12$ $6.715$ 12.12.$$\cdots$$.1 None $$0$$ $$0$$ $$8$$ $$10$$ $-$ $$q+\beta _{11}q^{2}+(-\beta _{6}-\beta _{9})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(841))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(841)) \simeq$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(29))$$$$^{\oplus 2}$$