Properties

 Label 390.2.p Level $390$ Weight $2$ Character orbit 390.p Rep. character $\chi_{390}(161,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $32$ Newform subspaces $7$ Sturm bound $168$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$390 = 2 \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 390.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(i)$$ Newform subspaces: $$7$$ Sturm bound: $$168$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(390, [\chi])$$.

Total New Old
Modular forms 184 32 152
Cusp forms 152 32 120
Eisenstein series 32 0 32

Trace form

 $$32 q + 24 q^{7} + O(q^{10})$$ $$32 q + 24 q^{7} - 8 q^{15} - 32 q^{16} - 16 q^{18} + 24 q^{19} + 8 q^{21} + 48 q^{27} - 24 q^{28} - 16 q^{31} - 8 q^{33} - 8 q^{34} - 40 q^{37} - 8 q^{39} - 48 q^{42} + 16 q^{45} + 8 q^{46} - 24 q^{52} + 48 q^{54} - 16 q^{55} + 48 q^{57} + 16 q^{58} - 8 q^{60} - 16 q^{61} - 8 q^{63} - 16 q^{66} + 72 q^{67} - 16 q^{72} + 72 q^{73} + 24 q^{76} + 24 q^{78} - 80 q^{79} - 64 q^{81} - 8 q^{84} + 48 q^{85} - 64 q^{87} + 40 q^{91} + 8 q^{93} + 80 q^{94} + 8 q^{97} - 48 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(390, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
390.2.p.a $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$12$$ $$q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.b $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$-12$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.c $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.d $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.e $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.f $4$ $3.114$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$
390.2.p.g $8$ $3.114$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(390, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(390, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$