# Properties

 Label 152.2.i Level $152$ Weight $2$ Character orbit 152.i Rep. character $\chi_{152}(49,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $10$ Newform subspaces $3$ Sturm bound $40$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 152.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$40$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(152, [\chi])$$.

Total New Old
Modular forms 48 10 38
Cusp forms 32 10 22
Eisenstein series 16 0 16

## Trace form

 $$10 q - 3 q^{3} - 4 q^{7} - 2 q^{9} + O(q^{10})$$ $$10 q - 3 q^{3} - 4 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{13} - 4 q^{15} - 8 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} + 18 q^{27} + 4 q^{29} - 24 q^{31} - 5 q^{33} - 12 q^{35} - 16 q^{37} - 8 q^{39} + 15 q^{41} + 10 q^{43} - 8 q^{45} - 6 q^{49} - 20 q^{51} + 16 q^{53} + 14 q^{55} - 38 q^{57} - 25 q^{59} + 12 q^{61} + 40 q^{63} - 4 q^{65} + 5 q^{67} + 20 q^{69} + 8 q^{71} + 29 q^{73} + 6 q^{75} + 20 q^{77} + 6 q^{79} - 25 q^{81} + 46 q^{83} + 6 q^{85} + 64 q^{87} + 12 q^{89} - 44 q^{91} - 36 q^{93} + 42 q^{95} + 11 q^{97} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(152, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.2.i.a $2$ $1.214$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-3$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$$
152.2.i.b $2$ $1.214$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$4$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$$
152.2.i.c $6$ $1.214$ 6.0.2696112.1 None $$0$$ $$-1$$ $$-1$$ $$-4$$ $$q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(152, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(152, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$