Properties

 Label 1078.2.i Level $1078$ Weight $2$ Character orbit 1078.i Rep. character $\chi_{1078}(901,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $4$ 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.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ 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 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

 $$80 q + 40 q^{4} + 12 q^{5} + 24 q^{9} + O(q^{10})$$ $$80 q + 40 q^{4} + 12 q^{5} + 24 q^{9} - 12 q^{11} + 24 q^{15} - 40 q^{16} + 16 q^{22} - 16 q^{23} + 56 q^{25} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 48 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{44} + 108 q^{45} - 24 q^{47} + 28 q^{53} + 12 q^{58} - 60 q^{59} + 12 q^{60} - 80 q^{64} - 48 q^{66} - 28 q^{67} - 24 q^{71} - 60 q^{75} - 12 q^{80} - 16 q^{81} - 28 q^{86} + 8 q^{88} - 96 q^{89} - 32 q^{92} + 76 q^{93} - 144 q^{99} + O(q^{100})$$

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.i.a $16$ $8.608$ $$\Q(\zeta_{48})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{48}q^{2}+(-\zeta_{48}^{2}+\zeta_{48}^{7}-\zeta_{48}^{10}+\cdots)q^{3}+\cdots$$
1078.2.i.b $16$ $8.608$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\beta _{1}q^{4}+\cdots$$
1078.2.i.c $16$ $8.608$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4}-\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots$$
1078.2.i.d $32$ $8.608$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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