# Properties

 Label 138.2.e Level $138$ Weight $2$ Character orbit 138.e Rep. character $\chi_{138}(13,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $40$ Newform subspaces $4$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$138 = 2 \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 138.e (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(138, [\chi])$$.

Total New Old
Modular forms 280 40 240
Cusp forms 200 40 160
Eisenstein series 80 0 80

## Trace form

 $$40 q - 4 q^{4} + 8 q^{5} + 8 q^{7} - 4 q^{9} + O(q^{10})$$ $$40 q - 4 q^{4} + 8 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{10} + 24 q^{11} + 16 q^{13} + 8 q^{14} + 8 q^{15} - 4 q^{16} - 20 q^{17} - 16 q^{19} - 36 q^{20} + 4 q^{21} - 32 q^{22} - 64 q^{23} - 52 q^{25} - 28 q^{26} - 36 q^{28} - 12 q^{29} + 12 q^{30} - 12 q^{31} + 12 q^{33} + 24 q^{34} + 20 q^{35} - 4 q^{36} - 16 q^{37} + 32 q^{38} - 36 q^{39} + 4 q^{40} - 12 q^{41} + 12 q^{42} + 16 q^{43} + 24 q^{44} + 8 q^{45} + 20 q^{46} - 48 q^{47} + 44 q^{49} + 24 q^{50} - 16 q^{51} + 16 q^{52} - 12 q^{53} - 24 q^{55} + 8 q^{56} - 32 q^{57} - 12 q^{58} + 20 q^{59} + 8 q^{60} - 28 q^{61} + 40 q^{62} + 8 q^{63} - 4 q^{64} + 64 q^{65} + 24 q^{66} + 8 q^{67} + 24 q^{68} + 20 q^{69} - 16 q^{70} + 72 q^{71} + 44 q^{73} + 8 q^{74} + 32 q^{75} + 28 q^{76} + 64 q^{77} + 16 q^{78} - 44 q^{79} + 8 q^{80} - 4 q^{81} - 4 q^{82} + 20 q^{83} + 4 q^{84} + 8 q^{85} + 40 q^{86} + 40 q^{87} + 12 q^{88} + 28 q^{89} + 4 q^{90} + 56 q^{91} + 24 q^{92} + 32 q^{93} + 24 q^{94} - 28 q^{95} + 68 q^{97} - 56 q^{98} - 20 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(138, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.2.e.a $10$ $1.102$ $$\Q(\zeta_{22})$$ None $$-1$$ $$-1$$ $$8$$ $$8$$ $$q-\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$$
138.2.e.b $10$ $1.102$ $$\Q(\zeta_{22})$$ None $$-1$$ $$1$$ $$-2$$ $$0$$ $$q-\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
138.2.e.c $10$ $1.102$ $$\Q(\zeta_{22})$$ None $$1$$ $$-1$$ $$0$$ $$-2$$ $$q+\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$$
138.2.e.d $10$ $1.102$ $$\Q(\zeta_{22})$$ None $$1$$ $$1$$ $$2$$ $$2$$ $$q+\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(138, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(138, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(46, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 2}$$