Properties

 Label 1600.2.q Level $1600$ Weight $2$ Character orbit 1600.q Rep. character $\chi_{1600}(49,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $68$ Newform subspaces $8$ Sturm bound $480$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1600.q (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Newform subspaces: $$8$$ Sturm bound: $$480$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1600, [\chi])$$.

Total New Old
Modular forms 528 76 452
Cusp forms 432 68 364
Eisenstein series 96 8 88

Trace form

 $$68 q + O(q^{10})$$ $$68 q + 4 q^{11} - 20 q^{19} + 8 q^{21} + 4 q^{29} + 32 q^{31} + 52 q^{49} + 28 q^{59} + 28 q^{61} - 40 q^{69} + 64 q^{79} - 44 q^{81} + 8 q^{91} + 84 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1600, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.2.q.a $2$ $12.776$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$-4$$ $$q+(-1-i)q^{3}-2q^{7}-iq^{9}+(-1+\cdots)q^{11}+\cdots$$
1600.2.q.b $2$ $12.776$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$4$$ $$q+(1+i)q^{3}+2q^{7}-iq^{9}+(-1-i)q^{11}+\cdots$$
1600.2.q.c $4$ $12.776$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+(-1+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$$
1600.2.q.d $4$ $12.776$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$2$$ $$0$$ $$-4$$ $$q+(\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$$
1600.2.q.e $12$ $12.776$ 12.0.$$\cdots$$.1 None $$0$$ $$-2$$ $$0$$ $$12$$ $$q+\beta _{4}q^{3}+(1+\beta _{5})q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
1600.2.q.f $12$ $12.776$ 12.0.$$\cdots$$.1 None $$0$$ $$2$$ $$0$$ $$-12$$ $$q-\beta _{4}q^{3}+(-1-\beta _{5})q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
1600.2.q.g $16$ $12.776$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{6}q^{3}+(-\beta _{6}+\beta _{9}+\beta _{10}+\beta _{15})q^{7}+\cdots$$
1600.2.q.h $16$ $12.776$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{6}q^{3}+(\beta _{6}-\beta _{9}-\beta _{10}-\beta _{15})q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1600, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1600, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 3}$$