# Properties

 Label 1425.2.c Level $1425$ Weight $2$ Character orbit 1425.c Rep. character $\chi_{1425}(799,\cdot)$ Character field $\Q$ Dimension $52$ Newform subspaces $16$ Sturm bound $400$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1425 = 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1425.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$16$$ Sturm bound: $$400$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1425, [\chi])$$.

Total New Old
Modular forms 212 52 160
Cusp forms 188 52 136
Eisenstein series 24 0 24

## Trace form

 $$52 q - 48 q^{4} - 4 q^{6} - 52 q^{9} + O(q^{10})$$ $$52 q - 48 q^{4} - 4 q^{6} - 52 q^{9} - 4 q^{11} - 32 q^{14} + 56 q^{16} + 8 q^{19} + 12 q^{24} + 8 q^{26} + 16 q^{29} + 24 q^{31} + 8 q^{34} + 48 q^{36} - 56 q^{41} + 8 q^{44} - 48 q^{46} - 40 q^{49} + 16 q^{51} + 4 q^{54} - 96 q^{59} - 28 q^{61} - 32 q^{64} - 16 q^{66} - 16 q^{69} + 96 q^{71} + 168 q^{74} - 20 q^{76} - 24 q^{79} + 52 q^{81} + 32 q^{84} - 8 q^{86} + 32 q^{89} - 32 q^{94} - 68 q^{96} + 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1425, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1425.2.c.a $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots$$
1425.2.c.b $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+5iq^{7}+\cdots$$
1425.2.c.c $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+2iq^{7}+\cdots$$
1425.2.c.d $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}-2iq^{7}+\cdots$$
1425.2.c.e $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots$$
1425.2.c.f $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots$$
1425.2.c.g $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots$$
1425.2.c.h $2$ $11.379$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots$$
1425.2.c.i $4$ $11.379$ $$\Q(i, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{1}q^{3}-5q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$$
1425.2.c.j $4$ $11.379$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
1425.2.c.k $4$ $11.379$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{3}q^{6}+\cdots$$
1425.2.c.l $4$ $11.379$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
1425.2.c.m $4$ $11.379$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$$
1425.2.c.n $4$ $11.379$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$$
1425.2.c.o $6$ $11.379$ 6.0.44836416.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots$$
1425.2.c.p $6$ $11.379$ 6.0.24681024.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1425, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1425, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$