# Properties

 Label 156.4.b Level $156$ Weight $4$ Character orbit 156.b Rep. character $\chi_{156}(25,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $112$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$156 = 2^{2} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 156.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$112$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(156, [\chi])$$.

Total New Old
Modular forms 90 6 84
Cusp forms 78 6 72
Eisenstein series 12 0 12

## Trace form

 $$6 q - 6 q^{3} + 54 q^{9} + O(q^{10})$$ $$6 q - 6 q^{3} + 54 q^{9} - 34 q^{13} - 92 q^{17} + 136 q^{23} + 166 q^{25} - 54 q^{27} + 116 q^{29} - 56 q^{35} - 54 q^{39} - 632 q^{43} + 1042 q^{49} + 492 q^{51} - 1572 q^{53} + 960 q^{55} - 628 q^{61} - 536 q^{65} - 120 q^{69} + 426 q^{75} + 1776 q^{77} - 1568 q^{79} + 486 q^{81} - 276 q^{87} - 1736 q^{91} - 4968 q^{95} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(156, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.4.b.a $2$ $9.204$ $$\Q(\sqrt{-3})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+9q^{9}+\cdots$$
156.4.b.b $4$ $9.204$ 4.0.47664588.1 None $$0$$ $$-12$$ $$0$$ $$0$$ $$q-3q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+9q^{9}+(-3\beta _{1}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(156, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(156, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$