# Properties

 Label 48.13.g Level $48$ Weight $13$ Character orbit 48.g Rep. character $\chi_{48}(31,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $3$ Sturm bound $104$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$13$$ Character orbit: $$[\chi]$$ $$=$$ 48.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$104$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{13}(48, [\chi])$$.

Total New Old
Modular forms 102 12 90
Cusp forms 90 12 78
Eisenstein series 12 0 12

## Trace form

 $$12 q + 30888 q^{5} - 2125764 q^{9} + O(q^{10})$$ $$12 q + 30888 q^{5} - 2125764 q^{9} - 8834760 q^{13} + 7258680 q^{17} + 75057840 q^{21} + 619612260 q^{25} - 1765403640 q^{29} - 966304080 q^{33} + 120720600 q^{37} + 10244732472 q^{41} - 5471716536 q^{45} + 23307267660 q^{49} - 60434995320 q^{53} + 19439980560 q^{57} - 175710390120 q^{61} + 332241524496 q^{65} + 506726668440 q^{73} - 1143003631680 q^{77} + 376572715308 q^{81} - 1463329887984 q^{85} + 2444968318104 q^{89} - 1744253397360 q^{93} + 3334060903320 q^{97} + O(q^{100})$$

## Decomposition of $$S_{13}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.13.g.a $4$ $43.872$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$0$$ $$0$$ $$-21960$$ $$0$$ $$q-3^{5}\beta _{1}q^{3}+(-5490-5\beta _{2})q^{5}+(-5372\beta _{1}+\cdots)q^{7}+\cdots$$
48.13.g.b $4$ $43.872$ $$\Q(\sqrt{-3}, \sqrt{-2803})$$ None $$0$$ $$0$$ $$22392$$ $$0$$ $$q+\beta _{1}q^{3}+(5598+\beta _{2})q^{5}+(-63\beta _{1}+\cdots)q^{7}+\cdots$$
48.13.g.c $4$ $43.872$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None $$0$$ $$0$$ $$30456$$ $$0$$ $$q+3^{5}\beta _{1}q^{3}+(7614-\beta _{2})q^{5}+(-15668\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{13}^{\mathrm{old}}(48, [\chi])$$ into lower level spaces

$$S_{13}^{\mathrm{old}}(48, [\chi]) \simeq$$ $$S_{13}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{13}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{13}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{13}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{13}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$