# Properties

 Label 3332.2.b Level $3332$ Weight $2$ Character orbit 3332.b Rep. character $\chi_{3332}(2549,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $6$ Sturm bound $1008$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3332.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1008$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3332, [\chi])$$.

Total New Old
Modular forms 528 62 466
Cusp forms 480 62 418
Eisenstein series 48 0 48

## Trace form

 $$62 q - 66 q^{9} + O(q^{10})$$ $$62 q - 66 q^{9} - 12 q^{13} + 12 q^{15} - 6 q^{17} - 4 q^{19} - 46 q^{25} - 12 q^{43} + 18 q^{51} + 40 q^{53} - 4 q^{55} + 24 q^{59} - 4 q^{67} - 48 q^{69} + 90 q^{81} - 4 q^{83} - 2 q^{85} - 44 q^{87} - 24 q^{89} - 4 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3332, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.2.b.a $2$ $26.606$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+2\beta q^{5}+q^{9}+\beta q^{11}+4q^{13}+\cdots$$
3332.2.b.b $8$ $26.606$ 8.0.980441344.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{7})q^{3}+\beta _{3}q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
3332.2.b.c $8$ $26.606$ 8.0.12960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{7}q^{5}+(-1-\beta _{1})q^{9}+\beta _{5}q^{11}+\cdots$$
3332.2.b.d $12$ $26.606$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$$
3332.2.b.e $12$ $26.606$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(-1+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$$
3332.2.b.f $20$ $26.606$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{3}-\beta _{14}q^{5}+(-2+\beta _{3})q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3332, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3332, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(119, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(238, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(476, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(833, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1666, [\chi])$$$$^{\oplus 2}$$