Properties

 Label 35.4.b Level $35$ Weight $4$ Character orbit 35.b Rep. character $\chi_{35}(29,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 35.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(35, [\chi])$$.

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

Trace form

 $$10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} + O(q^{10})$$ $$10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} - 16 q^{10} + 84 q^{11} - 56 q^{14} + 8 q^{15} + 148 q^{16} + 72 q^{19} - 68 q^{20} + 140 q^{21} + 72 q^{24} - 362 q^{25} - 620 q^{26} + 88 q^{29} + 52 q^{30} + 120 q^{31} + 964 q^{34} - 28 q^{35} - 420 q^{36} + 212 q^{39} + 1396 q^{40} - 852 q^{41} - 1424 q^{44} - 510 q^{45} + 176 q^{46} - 490 q^{49} + 1644 q^{50} + 1276 q^{51} - 996 q^{54} - 1136 q^{55} + 588 q^{56} + 864 q^{59} - 1692 q^{60} - 884 q^{61} - 2724 q^{64} + 520 q^{65} + 1148 q^{66} + 4808 q^{69} + 756 q^{70} + 880 q^{71} + 3024 q^{74} + 720 q^{75} - 2672 q^{76} - 3580 q^{79} - 2316 q^{80} - 302 q^{81} - 1904 q^{84} + 1572 q^{85} + 2432 q^{86} - 1492 q^{89} - 7748 q^{90} + 476 q^{91} + 1652 q^{94} - 1628 q^{95} + 4080 q^{96} - 5304 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.4.b.a $10$ $2.065$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$