# Properties

 Label 588.3.d Level $588$ Weight $3$ Character orbit 588.d Rep. character $\chi_{588}(97,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $3$ Sturm bound $336$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$588 = 2^{2} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 588.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$336$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(588, [\chi])$$.

Total New Old
Modular forms 248 14 234
Cusp forms 200 14 186
Eisenstein series 48 0 48

## Trace form

 $$14 q - 42 q^{9} + O(q^{10})$$ $$14 q - 42 q^{9} - 36 q^{11} + 24 q^{15} - 40 q^{23} - 6 q^{25} - 16 q^{29} + 26 q^{37} + 30 q^{39} - 22 q^{43} - 72 q^{51} - 240 q^{53} + 6 q^{57} + 12 q^{65} + 86 q^{67} + 20 q^{71} - 294 q^{79} + 126 q^{81} + 288 q^{85} + 42 q^{93} - 356 q^{95} + 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(588, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.3.d.a $2$ $16.022$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-\zeta_{6}q^{5}-3q^{9}-3q^{11}-4\zeta_{6}q^{13}+\cdots$$
588.3.d.b $4$ $16.022$ $$\Q(\sqrt{-3}, \sqrt{65})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{5}-3q^{9}+(-8+\cdots)q^{11}+\cdots$$
588.3.d.c $8$ $16.022$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{4}+\beta _{5})q^{5}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(588, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(588, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$