# Properties

 Label 2184.2.h Level $2184$ Weight $2$ Character orbit 2184.h Rep. character $\chi_{2184}(337,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $7$ Sturm bound $896$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2184.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$896$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2184, [\chi])$$.

Total New Old
Modular forms 464 44 420
Cusp forms 432 44 388
Eisenstein series 32 0 32

## Trace form

 $$44 q + 44 q^{9} + O(q^{10})$$ $$44 q + 44 q^{9} - 8 q^{13} - 16 q^{17} - 16 q^{23} - 36 q^{25} - 32 q^{29} + 8 q^{39} + 32 q^{43} - 44 q^{49} + 16 q^{51} + 16 q^{53} + 64 q^{55} + 32 q^{61} + 24 q^{79} + 44 q^{81} - 56 q^{87} - 4 q^{91} - 24 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2184, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2184.2.h.a $2$ $17.439$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+3iq^{5}+iq^{7}+q^{9}+5iq^{11}+\cdots$$
2184.2.h.b $2$ $17.439$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+3iq^{5}+iq^{7}+q^{9}-4iq^{11}+\cdots$$
2184.2.h.c $4$ $17.439$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-q^{3}-\beta _{2}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
2184.2.h.d $6$ $17.439$ 6.0.350464.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5})q^{5}+\cdots$$
2184.2.h.e $10$ $17.439$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$-10$$ $$0$$ $$0$$ $$q-q^{3}+(\beta _{1}+\beta _{5})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots$$
2184.2.h.f $10$ $17.439$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$10$$ $$0$$ $$0$$ $$q+q^{3}-\beta _{4}q^{5}+\beta _{7}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots$$
2184.2.h.g $10$ $17.439$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$10$$ $$0$$ $$0$$ $$q+q^{3}+(-\beta _{1}-\beta _{6})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2184, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2184, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(312, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(546, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(728, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1092, [\chi])$$$$^{\oplus 2}$$