Properties

 Label 192.3.i Level $192$ Weight $3$ Character orbit 192.i Rep. character $\chi_{192}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $28$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 192.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(192, [\chi])$$.

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

 $$28 q + 2 q^{3} + O(q^{10})$$ $$28 q + 2 q^{3} - 4 q^{13} + 4 q^{15} + 36 q^{19} + 16 q^{21} + 50 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{37} + 68 q^{43} - 52 q^{45} - 36 q^{49} - 96 q^{51} - 36 q^{61} - 192 q^{63} - 124 q^{67} - 20 q^{69} - 178 q^{75} - 248 q^{79} - 4 q^{81} - 64 q^{85} - 288 q^{91} - 68 q^{93} - 8 q^{97} + 292 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(192, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
192.3.i.a $$8$$ $$5.232$$ 8.0.629407744.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{3}+\cdots$$
192.3.i.b $$20$$ $$5.232$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(192, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(192, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 3}$$