# Properties

 Label 52.6.d Level $52$ Weight $6$ Character orbit 52.d Rep. character $\chi_{52}(25,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $42$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$52 = 2^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 52.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$42$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(52, [\chi])$$.

Total New Old
Modular forms 38 6 32
Cusp forms 32 6 26
Eisenstein series 6 0 6

## Trace form

 $$6 q + 706 q^{9} + O(q^{10})$$ $$6 q + 706 q^{9} - 730 q^{13} + 3440 q^{17} + 6368 q^{23} - 2726 q^{25} - 1368 q^{27} - 9092 q^{29} - 3400 q^{35} - 7288 q^{39} - 22208 q^{43} - 13346 q^{49} + 36440 q^{51} - 40332 q^{53} + 82032 q^{55} - 7492 q^{61} + 4004 q^{65} - 84520 q^{69} + 223240 q^{75} + 172824 q^{77} - 88304 q^{79} - 52538 q^{81} - 50096 q^{87} - 294128 q^{91} - 90720 q^{95} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(52, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
52.6.d.a $6$ $8.340$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(118+\beta _{3}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(52, [\chi])$$ into lower level spaces

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