# Properties

 Label 128.3.h Level $128$ Weight $3$ Character orbit 128.h Rep. character $\chi_{128}(15,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $28$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 128.h (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(128, [\chi])$$.

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

## Trace form

 $$28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
128.3.h.a $$28$$ $$3.488$$ None $$0$$ $$4$$ $$-4$$ $$4$$

## Decomposition of $$S_{3}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(128, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database