Properties

 Label 35.5.c Level $35$ Weight $5$ Character orbit 35.c Rep. character $\chi_{35}(34,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $5$ Sturm bound $20$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 35.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$20$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(35, [\chi])$$.

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

 $$14 q - 100 q^{4} + 264 q^{9} + O(q^{10})$$ $$14 q - 100 q^{4} + 264 q^{9} - 166 q^{11} - 360 q^{14} - 690 q^{15} + 1124 q^{16} + 54 q^{21} + 2450 q^{25} - 1606 q^{29} - 3300 q^{30} - 1010 q^{35} + 2868 q^{36} + 5478 q^{39} - 880 q^{44} - 21576 q^{46} - 2830 q^{49} + 10140 q^{50} + 5598 q^{51} + 18564 q^{56} + 11580 q^{60} - 6724 q^{64} - 23890 q^{65} - 2220 q^{70} - 20356 q^{71} + 23736 q^{74} + 37954 q^{79} - 13518 q^{81} - 67056 q^{84} + 22450 q^{85} + 14304 q^{86} + 36034 q^{91} + 3660 q^{95} - 53688 q^{99} + O(q^{100})$$

Decomposition of $$S_{5}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.5.c.a $1$ $3.618$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-17$$ $$25$$ $$49$$ $$q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots$$
35.5.c.b $1$ $3.618$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$17$$ $$-25$$ $$-49$$ $$q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots$$
35.5.c.c $2$ $3.618$ $$\Q(\sqrt{-6})$$ None $$0$$ $$-10$$ $$-10$$ $$-70$$ $$q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots$$
35.5.c.d $2$ $3.618$ $$\Q(\sqrt{-6})$$ None $$0$$ $$10$$ $$10$$ $$70$$ $$q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots$$
35.5.c.e $8$ $3.618$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots$$