# Properties

 Label 1078.2.c Level $1078$ Weight $2$ Character orbit 1078.c Rep. character $\chi_{1078}(1077,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $3$ Sturm bound $336$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$336$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1078, [\chi])$$.

Total New Old
Modular forms 184 40 144
Cusp forms 152 40 112
Eisenstein series 32 0 32

## Trace form

 $$40 q - 40 q^{4} - 24 q^{9} + O(q^{10})$$ $$40 q - 40 q^{4} - 24 q^{9} + 24 q^{15} + 40 q^{16} + 8 q^{22} - 32 q^{23} - 56 q^{25} + 24 q^{36} + 56 q^{53} + 24 q^{58} - 24 q^{60} - 40 q^{64} + 40 q^{67} - 24 q^{71} - 48 q^{78} - 56 q^{81} - 8 q^{86} - 8 q^{88} + 32 q^{92} - 40 q^{93} + 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1078, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1078.2.c.a $8$ $8.608$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}q^{2}+(-\zeta_{16}^{2}-\zeta_{16}^{4})q^{3}-q^{4}+\cdots$$
1078.2.c.b $16$ $8.608$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots$$
1078.2.c.c $16$ $8.608$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1078, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1078, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(539, [\chi])$$$$^{\oplus 2}$$