Properties

 Label 930.2.d Level $930$ Weight $2$ Character orbit 930.d Rep. character $\chi_{930}(559,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $9$ Sturm bound $384$ Trace bound $11$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$384$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(930, [\chi])$$.

Total New Old
Modular forms 200 28 172
Cusp forms 184 28 156
Eisenstein series 16 0 16

Trace form

 $$28 q - 28 q^{4} + 8 q^{5} - 28 q^{9} + O(q^{10})$$ $$28 q - 28 q^{4} + 8 q^{5} - 28 q^{9} - 8 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 16 q^{19} - 8 q^{20} + 24 q^{26} - 16 q^{29} - 16 q^{34} + 28 q^{36} + 24 q^{41} + 8 q^{44} - 8 q^{45} + 8 q^{46} - 20 q^{49} - 16 q^{50} + 8 q^{51} - 24 q^{55} + 8 q^{56} + 24 q^{59} + 8 q^{60} - 28 q^{64} - 40 q^{65} - 16 q^{66} + 16 q^{69} + 32 q^{71} - 8 q^{74} + 32 q^{75} - 16 q^{76} - 48 q^{79} + 8 q^{80} + 28 q^{81} - 24 q^{85} + 16 q^{86} - 72 q^{89} + 32 q^{91} + 56 q^{94} - 24 q^{95} + 8 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(930, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
930.2.d.a $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots$$
930.2.d.b $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$$
930.2.d.c $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}+q^{6}+\cdots$$
930.2.d.d $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots$$
930.2.d.e $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots$$
930.2.d.f $2$ $7.426$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots$$
930.2.d.g $4$ $7.426$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{8}q^{2}+\zeta_{8}q^{3}-q^{4}+(2+\zeta_{8})q^{5}+\cdots$$
930.2.d.h $6$ $7.426$ 6.0.3534400.1 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots$$
930.2.d.i $6$ $7.426$ 6.0.11669056.1 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(930, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(310, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$