# Properties

 Label 32.6.a Level $32$ Weight $6$ Character orbit 32.a Rep. character $\chi_{32}(1,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $4$ Sturm bound $24$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 32.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$24$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_0(32))$$.

Total New Old
Modular forms 24 5 19
Cusp forms 16 5 11
Eisenstein series 8 0 8

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

$$2$$Dim.
$$+$$$$2$$
$$-$$$$3$$

## Trace form

 $$5q + 38q^{5} + 449q^{9} + O(q^{10})$$ $$5q + 38q^{5} + 449q^{9} + 110q^{13} + 1610q^{17} - 5888q^{21} - 4277q^{25} + 3678q^{29} + 13184q^{33} - 7258q^{37} - 30766q^{41} + 63214q^{45} + 57789q^{49} - 76490q^{53} - 132992q^{57} + 108510q^{61} + 113476q^{65} - 226560q^{69} - 120318q^{73} + 195328q^{77} + 270029q^{81} - 131124q^{85} - 174702q^{89} + 152576q^{93} + 359642q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_0(32))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2
32.6.a.a $$1$$ $$5.132$$ $$\Q$$ None $$0$$ $$-8$$ $$14$$ $$-208$$ $$+$$ $$q-8q^{3}+14q^{5}-208q^{7}-179q^{9}+\cdots$$
32.6.a.b $$1$$ $$5.132$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-82$$ $$0$$ $$+$$ $$q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots$$
32.6.a.c $$1$$ $$5.132$$ $$\Q$$ None $$0$$ $$8$$ $$14$$ $$208$$ $$-$$ $$q+8q^{3}+14q^{5}+208q^{7}-179q^{9}+\cdots$$
32.6.a.d $$2$$ $$5.132$$ $$\Q(\sqrt{3})$$ None $$0$$ $$0$$ $$92$$ $$0$$ $$-$$ $$q+\beta q^{3}+46q^{5}-6\beta q^{7}+525q^{9}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_0(32))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_0(32)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_0(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_0(8))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_0(16))$$$$^{\oplus 2}$$