# Properties

 Label 1150.2.b Level $1150$ Weight $2$ Character orbit 1150.b Rep. character $\chi_{1150}(599,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $10$ Sturm bound $360$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1150 = 2 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1150.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$360$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1150, [\chi])$$.

Total New Old
Modular forms 192 32 160
Cusp forms 168 32 136
Eisenstein series 24 0 24

## Trace form

 $$32 q - 32 q^{4} - 4 q^{6} - 44 q^{9} + O(q^{10})$$ $$32 q - 32 q^{4} - 4 q^{6} - 44 q^{9} + 16 q^{11} + 32 q^{16} + 8 q^{19} - 16 q^{21} + 4 q^{24} - 24 q^{26} - 8 q^{31} + 20 q^{34} + 44 q^{36} + 16 q^{39} - 44 q^{41} - 16 q^{44} - 4 q^{46} - 16 q^{49} - 44 q^{51} + 52 q^{54} + 40 q^{59} - 60 q^{61} - 32 q^{64} - 44 q^{66} + 8 q^{69} - 24 q^{71} + 12 q^{74} - 8 q^{76} - 24 q^{79} + 48 q^{81} + 16 q^{84} + 20 q^{86} + 60 q^{89} + 8 q^{91} + 16 q^{94} - 4 q^{96} - 68 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1150, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1150.2.b.a $2$ $9.183$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-4iq^{7}+\cdots$$
1150.2.b.b $2$ $9.183$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots$$
1150.2.b.c $2$ $9.183$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots$$
1150.2.b.d $2$ $9.183$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-4iq^{7}+iq^{8}+3q^{9}+\cdots$$
1150.2.b.e $2$ $9.183$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots$$
1150.2.b.f $4$ $9.183$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots$$
1150.2.b.g $4$ $9.183$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots$$
1150.2.b.h $4$ $9.183$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots$$
1150.2.b.i $4$ $9.183$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$$
1150.2.b.j $6$ $9.183$ 6.0.77580864.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1150, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(575, [\chi])$$$$^{\oplus 2}$$