# Properties

 Label 121.4.a Level $121$ Weight $4$ Character orbit 121.a Rep. character $\chi_{121}(1,\cdot)$ Character field $\Q$ Dimension $23$ Newform subspaces $8$ Sturm bound $44$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$121 = 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 121.a (trivial) Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$44$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(121))$$.

Total New Old
Modular forms 39 32 7
Cusp forms 27 23 4
Eisenstein series 12 9 3

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

$$11$$Dim
$$+$$$$13$$
$$-$$$$10$$

## Trace form

 $$23 q - 2 q^{2} + 88 q^{4} + 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 107 q^{9} + O(q^{10})$$ $$23 q - 2 q^{2} + 88 q^{4} + 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 107 q^{9} - 50 q^{10} - 2 q^{12} - 80 q^{13} - 48 q^{14} + 232 q^{15} + 140 q^{16} + 124 q^{17} - 92 q^{18} - 72 q^{19} - 4 q^{20} - 76 q^{21} + 108 q^{23} - 252 q^{24} - 83 q^{25} + 32 q^{26} + 276 q^{27} + 128 q^{28} - 144 q^{29} + 266 q^{30} + 26 q^{31} + 104 q^{32} + 110 q^{34} + 172 q^{35} - 14 q^{36} - 102 q^{37} - 670 q^{38} - 400 q^{39} + 492 q^{40} - 536 q^{41} - 324 q^{42} + 60 q^{43} - 616 q^{45} + 314 q^{46} + 674 q^{47} - 1166 q^{48} + 125 q^{49} - 232 q^{50} + 164 q^{51} + 560 q^{52} + 266 q^{53} + 110 q^{54} + 156 q^{56} + 1512 q^{57} - 152 q^{58} - 832 q^{59} - 1300 q^{60} - 840 q^{61} - 134 q^{62} - 248 q^{63} - 1556 q^{64} + 880 q^{65} - 934 q^{67} - 640 q^{68} - 692 q^{69} - 428 q^{70} + 562 q^{71} + 744 q^{72} + 400 q^{73} - 6 q^{74} + 626 q^{75} - 432 q^{76} + 784 q^{78} - 316 q^{79} + 304 q^{80} - 169 q^{81} - 930 q^{82} - 468 q^{83} + 736 q^{84} - 452 q^{85} + 298 q^{86} - 1200 q^{87} + 1442 q^{89} - 1532 q^{90} + 2456 q^{91} + 1332 q^{92} + 4728 q^{93} + 992 q^{94} - 2952 q^{95} + 952 q^{96} + 1244 q^{97} + 870 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(121))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
121.4.a.a $1$ $7.139$ $$\Q$$ $$\Q(\sqrt{-11})$$ $$0$$ $$8$$ $$18$$ $$0$$ $+$ $$q+8q^{3}-8q^{4}+18q^{5}+37q^{9}-2^{6}q^{12}+\cdots$$
121.4.a.b $2$ $7.139$ $$\Q(\sqrt{3})$$ None $$-2$$ $$-8$$ $$-10$$ $$-8$$ $-$ $$q+(-1+\beta )q^{2}+(-4+\beta )q^{3}+(5-2\beta )q^{4}+\cdots$$
121.4.a.c $2$ $7.139$ $$\Q(\sqrt{3})$$ None $$-2$$ $$-2$$ $$2$$ $$-20$$ $-$ $$q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots$$
121.4.a.d $2$ $7.139$ $$\Q(\sqrt{26})$$ None $$0$$ $$-10$$ $$10$$ $$0$$ $+$ $$q+\beta q^{2}-5q^{3}+18q^{4}+5q^{5}-5\beta q^{6}+\cdots$$
121.4.a.e $2$ $7.139$ $$\Q(\sqrt{3})$$ None $$2$$ $$-8$$ $$-10$$ $$8$$ $-$ $$q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(5+2\beta )q^{4}+\cdots$$
121.4.a.f $4$ $7.139$ $$\Q(\sqrt{5}, \sqrt{37})$$ None $$-4$$ $$6$$ $$-11$$ $$-25$$ $-$ $$q+(-1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+\cdots$$
121.4.a.g $4$ $7.139$ $$\Q(\sqrt{5}, \sqrt{37})$$ None $$4$$ $$6$$ $$-11$$ $$25$$ $+$ $$q+(1+\beta _{1}+\beta _{2})q^{2}+(2+\beta _{2})q^{3}+(3+\cdots)q^{4}+\cdots$$
121.4.a.h $6$ $7.139$ 6.6.$$\cdots$$.1 None $$0$$ $$8$$ $$14$$ $$0$$ $+$ $$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(3+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(121))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(121)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(11))$$$$^{\oplus 2}$$