Properties

 Label 304.3.r Level $304$ Weight $3$ Character orbit 304.r Rep. character $\chi_{304}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $38$ Newform subspaces $4$ Sturm bound $120$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 304.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(304, [\chi])$$.

Total New Old
Modular forms 172 42 130
Cusp forms 148 38 110
Eisenstein series 24 4 20

Trace form

 $$38 q + 3 q^{3} - q^{5} + 20 q^{7} + 46 q^{9} + O(q^{10})$$ $$38 q + 3 q^{3} - q^{5} + 20 q^{7} + 46 q^{9} + 4 q^{11} - 3 q^{13} + 3 q^{15} + 23 q^{17} + 18 q^{19} - 30 q^{21} - 23 q^{23} - 76 q^{25} - 3 q^{29} - 90 q^{33} + 122 q^{35} - 26 q^{39} + 57 q^{41} - 63 q^{43} + 28 q^{45} - 47 q^{47} + 146 q^{49} - 141 q^{51} + 21 q^{53} + 50 q^{55} + 37 q^{57} + 3 q^{59} + 7 q^{61} + 236 q^{63} + 387 q^{67} + 75 q^{71} + 27 q^{73} - 120 q^{77} - 165 q^{79} - 187 q^{81} - 76 q^{83} - 47 q^{85} - 330 q^{87} + 141 q^{89} - 234 q^{91} + 104 q^{93} + 201 q^{95} + 249 q^{97} + 164 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(304, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
304.3.r.a $$4$$ $$8.283$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$2$$ $$-8$$ $$q+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+\cdots$$
304.3.r.b $$6$$ $$8.283$$ 6.0.6967728.1 None $$0$$ $$9$$ $$-2$$ $$0$$ $$q+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(2-\beta _{1}+\cdots)q^{5}+\cdots$$
304.3.r.c $$8$$ $$8.283$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-6$$ $$-1$$ $$12$$ $$q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots$$
304.3.r.d $$20$$ $$8.283$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$6$$ $$0$$ $$16$$ $$q-\beta _{1}q^{3}+(\beta _{4}-\beta _{19})q^{5}+(1+\beta _{3})q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(304, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(304, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 2}$$