# Properties

 Label 975.2.c Level $975$ Weight $2$ Character orbit 975.c Rep. character $\chi_{975}(274,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $11$ Sturm bound $280$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$975 = 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 975.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$11$$ Sturm bound: $$280$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(975, [\chi])$$.

Total New Old
Modular forms 152 36 116
Cusp forms 128 36 92
Eisenstein series 24 0 24

## Trace form

 $$36 q - 44 q^{4} + 4 q^{6} - 36 q^{9} + O(q^{10})$$ $$36 q - 44 q^{4} + 4 q^{6} - 36 q^{9} - 8 q^{11} + 24 q^{14} + 52 q^{16} - 8 q^{21} - 12 q^{24} - 8 q^{29} + 32 q^{34} + 44 q^{36} + 8 q^{39} + 16 q^{41} + 112 q^{44} - 40 q^{46} - 28 q^{49} + 24 q^{51} - 4 q^{54} - 72 q^{56} + 16 q^{59} + 16 q^{61} - 76 q^{64} + 40 q^{66} - 40 q^{69} + 16 q^{71} + 80 q^{74} + 32 q^{76} - 24 q^{79} + 36 q^{81} + 8 q^{84} - 40 q^{86} - 8 q^{89} - 8 q^{91} + 8 q^{94} - 12 q^{96} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(975, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
975.2.c.a $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots$$
975.2.c.b $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-3iq^{7}+\cdots$$
975.2.c.c $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-iq^{7}+\cdots$$
975.2.c.d $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots$$
975.2.c.e $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+3iq^{8}+\cdots$$
975.2.c.f $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots$$
975.2.c.g $2$ $7.785$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots$$
975.2.c.h $4$ $7.785$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
975.2.c.i $6$ $7.785$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-3+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots$$
975.2.c.j $6$ $7.785$ 6.0.5089536.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots$$
975.2.c.k $6$ $7.785$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(975, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(975, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 2}$$