# Properties

 Label 1450.2.b Level $1450$ Weight $2$ Character orbit 1450.b Rep. character $\chi_{1450}(349,\cdot)$ Character field $\Q$ Dimension $42$ Newform subspaces $12$ Sturm bound $450$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1450 = 2 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1450.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$450$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1450, [\chi])$$.

Total New Old
Modular forms 238 42 196
Cusp forms 214 42 172
Eisenstein series 24 0 24

## Trace form

 $$42 q - 42 q^{4} - 34 q^{9} + O(q^{10})$$ $$42 q - 42 q^{4} - 34 q^{9} - 4 q^{11} + 42 q^{16} + 4 q^{19} - 16 q^{21} - 4 q^{26} + 6 q^{29} - 32 q^{31} + 34 q^{36} + 32 q^{39} + 24 q^{41} + 4 q^{44} - 16 q^{46} - 34 q^{49} + 28 q^{51} + 24 q^{54} - 12 q^{59} + 20 q^{61} - 42 q^{64} - 60 q^{66} + 56 q^{69} - 56 q^{71} - 24 q^{74} - 4 q^{76} - 56 q^{79} - 6 q^{81} + 16 q^{84} - 4 q^{86} + 88 q^{89} + 32 q^{91} - 24 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1450, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1450.2.b.a $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+2iq^{7}+\cdots$$
1450.2.b.b $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots$$
1450.2.b.c $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots$$
1450.2.b.d $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-2iq^{7}+iq^{8}+3q^{9}+\cdots$$
1450.2.b.e $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$$
1450.2.b.f $2$ $11.578$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+3iq^{3}-q^{4}+3q^{6}-2iq^{7}+\cdots$$
1450.2.b.g $4$ $11.578$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots$$
1450.2.b.h $4$ $11.578$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots$$
1450.2.b.i $4$ $11.578$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
1450.2.b.j $6$ $11.578$ 6.0.14077504.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots$$
1450.2.b.k $6$ $11.578$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1450.2.b.l $6$ $11.578$ 6.0.24681024.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1450, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1450, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(290, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(725, [\chi])$$$$^{\oplus 2}$$