Properties

 Label 390.2.bb Level $390$ Weight $2$ Character orbit 390.bb Rep. character $\chi_{390}(121,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $3$ Sturm bound $168$ Trace bound $10$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$390 = 2 \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 390.bb (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$168$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$7$$

Dimensions

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

Total New Old
Modular forms 184 16 168
Cusp forms 152 16 136
Eisenstein series 32 0 32

Trace form

 $$16 q + 8 q^{4} - 8 q^{9} + O(q^{10})$$ $$16 q + 8 q^{4} - 8 q^{9} - 4 q^{10} + 12 q^{11} - 8 q^{13} + 24 q^{14} - 8 q^{16} + 16 q^{17} + 12 q^{19} - 16 q^{25} - 16 q^{26} - 8 q^{29} - 4 q^{30} + 4 q^{35} + 8 q^{36} + 24 q^{37} - 4 q^{39} - 8 q^{40} + 8 q^{42} - 8 q^{43} - 12 q^{46} + 12 q^{49} - 32 q^{51} + 8 q^{52} - 16 q^{53} - 12 q^{55} + 12 q^{56} - 24 q^{58} + 24 q^{59} - 8 q^{61} + 8 q^{62} - 16 q^{64} - 20 q^{65} - 8 q^{66} + 24 q^{67} - 16 q^{68} + 8 q^{69} - 72 q^{71} + 4 q^{74} + 12 q^{76} + 16 q^{77} + 16 q^{78} - 8 q^{79} - 8 q^{81} - 8 q^{82} - 8 q^{87} + 12 q^{89} + 8 q^{90} + 20 q^{91} + 48 q^{93} - 16 q^{94} + 16 q^{95} + 48 q^{98} + O(q^{100})$$

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.bb.a $4$ $3.114$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
390.2.bb.b $4$ $3.114$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
390.2.bb.c $8$ $3.114$ 8.0.$$\cdots$$.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-\beta _{6}q^{3}+(1-\beta _{6})q^{4}-\beta _{2}q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(390, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$