# Properties

 Label 1725.2.b Level $1725$ Weight $2$ Character orbit 1725.b Rep. character $\chi_{1725}(1174,\cdot)$ Character field $\Q$ Dimension $64$ Newform subspaces $21$ Sturm bound $480$ Trace bound $14$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1725 = 3 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1725.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$21$$ Sturm bound: $$480$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1725, [\chi])$$.

Total New Old
Modular forms 252 64 188
Cusp forms 228 64 164
Eisenstein series 24 0 24

## Trace form

 $$64 q - 60 q^{4} - 4 q^{6} - 64 q^{9} + O(q^{10})$$ $$64 q - 60 q^{4} - 4 q^{6} - 64 q^{9} - 8 q^{14} + 68 q^{16} + 4 q^{19} - 4 q^{21} + 12 q^{24} + 8 q^{26} + 24 q^{29} - 28 q^{31} - 8 q^{34} + 60 q^{36} + 20 q^{39} - 64 q^{41} + 24 q^{44} - 8 q^{46} - 28 q^{49} + 4 q^{54} + 48 q^{56} - 48 q^{59} - 52 q^{61} - 44 q^{64} + 32 q^{66} + 8 q^{69} + 56 q^{71} + 112 q^{74} + 8 q^{76} - 8 q^{79} + 64 q^{81} - 32 q^{84} + 96 q^{86} + 72 q^{89} + 20 q^{91} + 40 q^{94} - 28 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1725, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1725.2.b.a $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+5iq^{7}+\cdots$$
1725.2.b.b $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots$$
1725.2.b.c $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots$$
1725.2.b.d $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+5iq^{7}+\cdots$$
1725.2.b.e $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{7}+\cdots$$
1725.2.b.f $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots$$
1725.2.b.g $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}-2iq^{7}+\cdots$$
1725.2.b.h $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots$$
1725.2.b.i $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}-iq^{7}-q^{9}-6q^{11}+\cdots$$
1725.2.b.j $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{4}+3iq^{7}-q^{9}-4q^{11}+\cdots$$
1725.2.b.k $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{4}-3iq^{7}-q^{9}+2q^{11}+\cdots$$
1725.2.b.l $2$ $13.774$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}-iq^{7}-q^{9}+4q^{11}+\cdots$$
1725.2.b.m $4$ $13.774$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{1}q^{3}-4q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots$$
1725.2.b.n $4$ $13.774$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
1725.2.b.o $4$ $13.774$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$$
1725.2.b.p $4$ $13.774$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots$$
1725.2.b.q $4$ $13.774$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$$
1725.2.b.r $4$ $13.774$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$$
1725.2.b.s $4$ $13.774$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
1725.2.b.t $6$ $13.774$ 6.0.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots$$
1725.2.b.u $6$ $13.774$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{1})q^{4}+\beta _{3}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1725, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1725, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(345, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(575, [\chi])$$$$^{\oplus 2}$$